吴代业发明《中国网眼筛子》，将不可能实现的埃氏筛法，巧妙，直观地予以实现

重生888@

时空伴随者
什么乱七八糟的，足够大是多大呢？质数表是客观存在，没有新旧之分。

什么乱七八糟，？没入门，当然乱七八糟！您写代码，我也认为乱七八糟。

重生888@

足够大，就是您想达到多大，就多大！只要在世界第一，18位数够了吧》关于新旧的质数表，旧质数表不是一个个写出来的数码吗，？新型质数就是一个个0.

重生888@

时空伴随者
有一点，您肯定不知道，当位数充分大时，素数是相当相当稀疏的，与其写出长长的01串，根本比不上直接写出素数的数码来得经济实惠

先生不相信，不要说人说梦话。我有10000以内的（新型质数表），两张A4纸就装满10000以内的全部质数和不易识别的合数，一个个写八张纸都不行！再说，它还包括不易识别的合数。地球绕着太阳转是梦话，还是太阳绕地球转是梦话？

重生888@

质数空洞是可以删去的！首先它可以降低30分之一，存储容易，查找容易！10000以内就有10个连续合数可删。

重生888@

外国足够大的素数数据库，中国人是拿不到的，必须自己做！先生举的几个数字，在吴代业《新型质数表》中，就是几个空格（0）.

这就如同建造高楼时无法直接套用外国的预制件一样，我国数学界必须在自己的土地上硬生生把地基打牢。既然现有的庞大资料对我们来说是“死数据”，那就得靠我们自己创造鲜活的成果。这不仅是填补书页上的空白，更是为了确立中国人在世界顶级科学版图中的坐标。那种不得不自己动手做表的紧迫感，恰恰折射出我们独立研究精神的坚韧与迫切。未来，随着计算能力的提升和方法论的创新，那些曾经冰冷的零号位格，终将被一个个闪耀的数字所填满。

时空伴随者

楼主老眼昏花，我举的是1405组四生素数，不是几个空格就能标识的。
从10^18开始的10^9个正整数内，有多少四生素数呢？
2026-10-01 13:27:42
1: 1000000000000430711
2: 1000000000000513661
3: 1000000000000925381
4: 1000000000001280581
5: 1000000000002081311
6: 1000000000002142751
7: 1000000000003453871
8: 1000000000004392061
9: 1000000000004815751
10: 1000000000005224501
11: 1000000000005770081
12: 1000000000006030811
13: 1000000000006859231
14: 1000000000007366591
15: 1000000000008091961
16: 1000000000008187691
17: 1000000000008224981
18: 1000000000008358331
19: 1000000000008772151
20: 1000000000010046641
21: 1000000000010775551
22: 1000000000010914361
23: 1000000000011731261
24: 1000000000011977351
25: 1000000000012782071
26: 1000000000012999751
27: 1000000000013702921
28: 1000000000013716391
29: 1000000000014072971
30: 1000000000014384371
31: 1000000000014477221
32: 1000000000016226611
33: 1000000000016777231
34: 1000000000017063371
35: 1000000000017442511
36: 1000000000018388021
37: 1000000000019520761
38: 1000000000019945801
39: 1000000000020555881
40: 1000000000020622421
41: 1000000000020765641
42: 1000000000020834731
43: 1000000000021398911
44: 1000000000022047391
45: 1000000000022163401
46: 1000000000022743451
47: 1000000000023475271
48: 1000000000023478871
49: 1000000000025769131
50: 1000000000026745511
51: 1000000000026806321
52: 1000000000026885461
53: 1000000000028949971
54: 1000000000029124271
55: 1000000000029135431
56: 1000000000029165851
57: 1000000000029535781
58: 1000000000030445831
59: 1000000000030910231
60: 1000000000031416451
61: 1000000000031759471
62: 1000000000034022101
63: 1000000000034446751
64: 1000000000035482051
65: 1000000000035778121
66: 1000000000037117531
67: 1000000000037787641
68: 1000000000040074931
69: 1000000000041424091
70: 1000000000041743711
71: 1000000000041821291
72: 1000000000044764261
73: 1000000000044836891
74: 1000000000044978131
75: 1000000000045453991
76: 1000000000045557611
77: 1000000000048327121
78: 1000000000048452911
79: 1000000000050031031
80: 1000000000050276101
81: 1000000000050959261
82: 1000000000052506631
83: 1000000000052883251
84: 1000000000053000251
85: 1000000000054829861
86: 1000000000056153071
87: 1000000000056686591
88: 1000000000057140911
89: 1000000000057370951
90: 1000000000058784161
91: 1000000000059328571
92: 1000000000062862151
93: 1000000000063305251
94: 1000000000063328021
95: 1000000000064209811
96: 1000000000064638451
97: 1000000000066102961
98: 1000000000066304351
99: 1000000000067524271
100: 1000000000068080111
……
1400: 1000000000992849161
1401: 1000000000994288681
1402: 1000000000997022671
1403: 1000000000998484091
1404: 1000000000999220651
1405: 1000000000999379111
用时 109.64494 秒

时空伴随者

从10^18开始的10^9个正整数内，有多少最密五生素数呢？
2026-10-03 21:59:27
1: 1000000000008224977, 1000000000008224981, 1000000000008224983, 1000000000008224987, 1000000000008224989
2: 1000000000021398907, 1000000000021398911, 1000000000021398913, 1000000000021398917, 1000000000021398919
3: 1000000000030910227, 1000000000030910231, 1000000000030910233, 1000000000030910237, 1000000000030910239
4: 1000000000041821287, 1000000000041821291, 1000000000041821293, 1000000000041821297, 1000000000041821299
5: 1000000000048327121, 1000000000048327123, 1000000000048327127, 1000000000048327129, 1000000000048327133
6: 1000000000052506631, 1000000000052506633, 1000000000052506637, 1000000000052506639, 1000000000052506643
7: 1000000000053000251, 1000000000053000253, 1000000000053000257, 1000000000053000259, 1000000000053000263
8: 1000000000073839901, 1000000000073839903, 1000000000073839907, 1000000000073839909, 1000000000073839913
9: 1000000000076867677, 1000000000076867681, 1000000000076867683, 1000000000076867687, 1000000000076867689
10: 1000000000079062897, 1000000000079062901, 1000000000079062903, 1000000000079062907, 1000000000079062909
11: 1000000000081245341, 1000000000081245343, 1000000000081245347, 1000000000081245349, 1000000000081245353
12: 1000000000086325151, 1000000000086325153, 1000000000086325157, 1000000000086325159, 1000000000086325163
13: 1000000000089368977, 1000000000089368981, 1000000000089368983, 1000000000089368987, 1000000000089368989
14: 1000000000105783421, 1000000000105783423, 1000000000105783427, 1000000000105783429, 1000000000105783433
15: 1000000000109402647, 1000000000109402651, 1000000000109402653, 1000000000109402657, 1000000000109402659
16: 1000000000114602577, 1000000000114602581, 1000000000114602583, 1000000000114602587, 1000000000114602589
17: 1000000000119099431, 1000000000119099433, 1000000000119099437, 1000000000119099439, 1000000000119099443
18: 1000000000124163671, 1000000000124163673, 1000000000124163677, 1000000000124163679, 1000000000124163683
19: 1000000000130965147, 1000000000130965151, 1000000000130965153, 1000000000130965157, 1000000000130965159
20: 1000000000142217071, 1000000000142217073, 1000000000142217077, 1000000000142217079, 1000000000142217083
21: 1000000000143382747, 1000000000143382751, 1000000000143382753, 1000000000143382757, 1000000000143382759
22: 1000000000147222511, 1000000000147222513, 1000000000147222517, 1000000000147222519, 1000000000147222523
23: 1000000000153664591, 1000000000153664593, 1000000000153664597, 1000000000153664599, 1000000000153664603
24: 1000000000156117391, 1000000000156117393, 1000000000156117397, 1000000000156117399, 1000000000156117403
25: 1000000000162656667, 1000000000162656671, 1000000000162656673, 1000000000162656677, 1000000000162656679
26: 1000000000164670357, 1000000000164670361, 1000000000164670363, 1000000000164670367, 1000000000164670369
27: 1000000000165348571, 1000000000165348573, 1000000000165348577, 1000000000165348579, 1000000000165348583
28: 1000000000167903011, 1000000000167903013, 1000000000167903017, 1000000000167903019, 1000000000167903023
29: 1000000000176236951, 1000000000176236953, 1000000000176236957, 1000000000176236959, 1000000000176236963
30: 1000000000178589997, 1000000000178590001, 1000000000178590003, 1000000000178590007, 1000000000178590009
31: 1000000000185449561, 1000000000185449563, 1000000000185449567, 1000000000185449569, 1000000000185449573
32: 1000000000195838017, 1000000000195838021, 1000000000195838023, 1000000000195838027, 1000000000195838029
33: 1000000000196746267, 1000000000196746271, 1000000000196746273, 1000000000196746277, 1000000000196746279
34: 1000000000210160347, 1000000000210160351, 1000000000210160353, 1000000000210160357, 1000000000210160359
35: 1000000000210160351, 1000000000210160353, 1000000000210160357, 1000000000210160359, 1000000000210160363
36: 1000000000210371697, 1000000000210371701, 1000000000210371703, 1000000000210371707, 1000000000210371709
37: 1000000000221082031, 1000000000221082033, 1000000000221082037, 1000000000221082039, 1000000000221082043
38: 1000000000226876017, 1000000000226876021, 1000000000226876023, 1000000000226876027, 1000000000226876029
39: 1000000000230259537, 1000000000230259541, 1000000000230259543, 1000000000230259547, 1000000000230259549
40: 1000000000232853791, 1000000000232853793, 1000000000232853797, 1000000000232853799, 1000000000232853803
41: 1000000000238762681, 1000000000238762683, 1000000000238762687, 1000000000238762689, 1000000000238762693
42: 1000000000239850777, 1000000000239850781, 1000000000239850783, 1000000000239850787, 1000000000239850789
43: 1000000000243949977, 1000000000243949981, 1000000000243949983, 1000000000243949987, 1000000000243949989
44: 1000000000247885467, 1000000000247885471, 1000000000247885473, 1000000000247885477, 1000000000247885479
45: 1000000000248443471, 1000000000248443473, 1000000000248443477, 1000000000248443479, 1000000000248443483
46: 1000000000251215857, 1000000000251215861, 1000000000251215863, 1000000000251215867, 1000000000251215869
47: 1000000000255870837, 1000000000255870841, 1000000000255870843, 1000000000255870847, 1000000000255870849
48: 1000000000270299641, 1000000000270299643, 1000000000270299647, 1000000000270299649, 1000000000270299653
49: 1000000000275129641, 1000000000275129643, 1000000000275129647, 1000000000275129649, 1000000000275129653
50: 1000000000293759581, 1000000000293759583, 1000000000293759587, 1000000000293759589, 1000000000293759593
51: 1000000000296965111, 1000000000296965113, 1000000000296965117, 1000000000296965119, 1000000000296965123
52: 1000000000305882337, 1000000000305882341, 1000000000305882343, 1000000000305882347, 1000000000305882349
53: 1000000000316406487, 1000000000316406491, 1000000000316406493, 1000000000316406497, 1000000000316406499
54: 1000000000336822181, 1000000000336822183, 1000000000336822187, 1000000000336822189, 1000000000336822193
55: 1000000000338901691, 1000000000338901693, 1000000000338901697, 1000000000338901699, 1000000000338901703
56: 1000000000342251277, 1000000000342251281, 1000000000342251283, 1000000000342251287, 1000000000342251289
57: 1000000000343057711, 1000000000343057713, 1000000000343057717, 1000000000343057719, 1000000000343057723
58: 1000000000365341861, 1000000000365341863, 1000000000365341867, 1000000000365341869, 1000000000365341873
59: 1000000000366226467, 1000000000366226471, 1000000000366226473, 1000000000366226477, 1000000000366226479
60: 1000000000388957411, 1000000000388957413, 1000000000388957417, 1000000000388957419, 1000000000388957423
61: 1000000000395803411, 1000000000395803413, 1000000000395803417, 1000000000395803419, 1000000000395803423
62: 1000000000409241277, 1000000000409241281, 1000000000409241283, 1000000000409241287, 1000000000409241289
63: 1000000000426453121, 1000000000426453123, 1000000000426453127, 1000000000426453129, 1000000000426453133
64: 1000000000433954617, 1000000000433954621, 1000000000433954623, 1000000000433954627, 1000000000433954629
65: 1000000000439566031, 1000000000439566033, 1000000000439566037, 1000000000439566039, 1000000000439566043
66: 1000000000439726051, 1000000000439726053, 1000000000439726057, 1000000000439726059, 1000000000439726063
67: 1000000000447465477, 1000000000447465481, 1000000000447465483, 1000000000447465487, 1000000000447465489
68: 1000000000468054121, 1000000000468054123, 1000000000468054127, 1000000000468054129, 1000000000468054133
69: 1000000000469982431, 1000000000469982433, 1000000000469982437, 1000000000469982439, 1000000000469982443
70: 1000000000491180037, 1000000000491180041, 1000000000491180043, 1000000000491180047, 1000000000491180049
71: 1000000000494779651, 1000000000494779653, 1000000000494779657, 1000000000494779659, 1000000000494779663
72: 1000000000500830467, 1000000000500830471, 1000000000500830473, 1000000000500830477, 1000000000500830479
73: 1000000000513519717, 1000000000513519721, 1000000000513519723, 1000000000513519727, 1000000000513519729
74: 1000000000516538467, 1000000000516538471, 1000000000516538473, 1000000000516538477, 1000000000516538479
75: 1000000000524746981, 1000000000524746983, 1000000000524746987, 1000000000524746989, 1000000000524746993
76: 1000000000526741561, 1000000000526741563, 1000000000526741567, 1000000000526741569, 1000000000526741573
77: 1000000000530153431, 1000000000530153433, 1000000000530153437, 1000000000530153439, 1000000000530153443
78: 1000000000531417177, 1000000000531417181, 1000000000531417183, 1000000000531417187, 1000000000531417189
79: 1000000000532096351, 1000000000532096353, 1000000000532096357, 1000000000532096359, 1000000000532096363
80: 1000000000536773437, 1000000000536773441, 1000000000536773443, 1000000000536773447, 1000000000536773449
81: 1000000000547078801, 1000000000547078803, 1000000000547078807, 1000000000547078809, 1000000000547078813
82: 1000000000549030841, 1000000000549030843, 1000000000549030847, 1000000000549030849, 1000000000549030853
83: 1000000000560138367, 1000000000560138371, 1000000000560138373, 1000000000560138377, 1000000000560138379
84: 1000000000562352067, 1000000000562352071, 1000000000562352073, 1000000000562352077, 1000000000562352079
85: 1000000000569691567, 1000000000569691571, 1000000000569691573, 1000000000569691577, 1000000000569691579
86: 1000000000572710771, 1000000000572710773, 1000000000572710777, 1000000000572710779, 1000000000572710783
87: 1000000000582633481, 1000000000582633483, 1000000000582633487, 1000000000582633489, 1000000000582633493
88: 1000000000584610297, 1000000000584610301, 1000000000584610303, 1000000000584610307, 1000000000584610309
89: 1000000000584922867, 1000000000584922871, 1000000000584922873, 1000000000584922877, 1000000000584922879
90: 1000000000587472597, 1000000000587472601, 1000000000587472603, 1000000000587472607, 1000000000587472609
91: 1000000000595427697, 1000000000595427701, 1000000000595427703, 1000000000595427707, 1000000000595427709
92: 1000000000603031501, 1000000000603031503, 1000000000603031507, 1000000000603031509, 1000000000603031513
93: 1000000000603332097, 1000000000603332101, 1000000000603332103, 1000000000603332107, 1000000000603332109
94: 1000000000609938397, 1000000000609938401, 1000000000609938403, 1000000000609938407, 1000000000609938409
95: 1000000000618236217, 1000000000618236221, 1000000000618236223, 1000000000618236227, 1000000000618236229
96: 1000000000626600217, 1000000000626600221, 1000000000626600223, 1000000000626600227, 1000000000626600229
97: 1000000000626777251, 1000000000626777253, 1000000000626777257, 1000000000626777259, 1000000000626777263
98: 1000000000627397501, 1000000000627397503, 1000000000627397507, 1000000000627397509, 1000000000627397513
99: 1000000000633639297, 1000000000633639301, 1000000000633639303, 1000000000633639307, 1000000000633639309
100: 1000000000636441031, 1000000000636441033, 1000000000636441037, 1000000000636441039, 1000000000636441043
101: 1000000000636821637, 1000000000636821641, 1000000000636821643, 1000000000636821647, 1000000000636821649
102: 1000000000651383157, 1000000000651383161, 1000000000651383163, 1000000000651383167, 1000000000651383169
103: 1000000000653191137, 1000000000653191141, 1000000000653191143, 1000000000653191147, 1000000000653191149
104: 1000000000663756901, 1000000000663756903, 1000000000663756907, 1000000000663756909, 1000000000663756913
105: 1000000000665406121, 1000000000665406123, 1000000000665406127, 1000000000665406129, 1000000000665406133
106: 1000000000675070947, 1000000000675070951, 1000000000675070953, 1000000000675070957, 1000000000675070959
107: 1000000000675070951, 1000000000675070953, 1000000000675070957, 1000000000675070959, 1000000000675070963
108: 1000000000684075207, 1000000000684075211, 1000000000684075213, 1000000000684075217, 1000000000684075219
109: 1000000000684930781, 1000000000684930783, 1000000000684930787, 1000000000684930789, 1000000000684930793
110: 1000000000687013861, 1000000000687013863, 1000000000687013867, 1000000000687013869, 1000000000687013873
111: 1000000000690100231, 1000000000690100233, 1000000000690100237, 1000000000690100239, 1000000000690100243
112: 1000000000696404551, 1000000000696404553, 1000000000696404557, 1000000000696404559, 1000000000696404563
113: 1000000000714150687, 1000000000714150691, 1000000000714150693, 1000000000714150697, 1000000000714150699
114: 1000000000724006531, 1000000000724006533, 1000000000724006537, 1000000000724006539, 1000000000724006543
115: 1000000000730756021, 1000000000730756023, 1000000000730756027, 1000000000730756029, 1000000000730756033
116: 1000000000731161321, 1000000000731161323, 1000000000731161327, 1000000000731161329, 1000000000731161333
117: 1000000000744661167, 1000000000744661171, 1000000000744661173, 1000000000744661177, 1000000000744661179
118: 1000000000748298157, 1000000000748298161, 1000000000748298163, 1000000000748298167, 1000000000748298169
119: 1000000000748716057, 1000000000748716061, 1000000000748716063, 1000000000748716067, 1000000000748716069
120: 1000000000754875061, 1000000000754875063, 1000000000754875067, 1000000000754875069, 1000000000754875073
121: 1000000000756712947, 1000000000756712951, 1000000000756712953, 1000000000756712957, 1000000000756712959
122: 1000000000758543217, 1000000000758543221, 1000000000758543223, 1000000000758543227, 1000000000758543229
123: 1000000000768057271, 1000000000768057273, 1000000000768057277, 1000000000768057279, 1000000000768057283
124: 1000000000771081567, 1000000000771081571, 1000000000771081573, 1000000000771081577, 1000000000771081579
125: 1000000000771485941, 1000000000771485943, 1000000000771485947, 1000000000771485949, 1000000000771485953
126: 1000000000775047031, 1000000000775047033, 1000000000775047037, 1000000000775047039, 1000000000775047043
127: 1000000000779413317, 1000000000779413321, 1000000000779413323, 1000000000779413327, 1000000000779413329
128: 1000000000783857247, 1000000000783857251, 1000000000783857253, 1000000000783857257, 1000000000783857259
129: 1000000000790349101, 1000000000790349103, 1000000000790349107, 1000000000790349109, 1000000000790349113
130: 1000000000795698431, 1000000000795698433, 1000000000795698437, 1000000000795698439, 1000000000795698443
131: 1000000000797470917, 1000000000797470921, 1000000000797470923, 1000000000797470927, 1000000000797470929
132: 1000000000810851577, 1000000000810851581, 1000000000810851583, 1000000000810851587, 1000000000810851589
133: 1000000000850927047, 1000000000850927051, 1000000000850927053, 1000000000850927057, 1000000000850927059
134: 1000000000853330921, 1000000000853330923, 1000000000853330927, 1000000000853330929, 1000000000853330933
135: 1000000000866596621, 1000000000866596623, 1000000000866596627, 1000000000866596629, 1000000000866596633
136: 1000000000873715197, 1000000000873715201, 1000000000873715203, 1000000000873715207, 1000000000873715209
137: 1000000000885454287, 1000000000885454291, 1000000000885454293, 1000000000885454297, 1000000000885454299
138: 1000000000891394137, 1000000000891394141, 1000000000891394143, 1000000000891394147, 1000000000891394149
139: 1000000000895948861, 1000000000895948863, 1000000000895948867, 1000000000895948869, 1000000000895948873
140: 1000000000897891447, 1000000000897891451, 1000000000897891453, 1000000000897891457, 1000000000897891459
141: 1000000000901240741, 1000000000901240743, 1000000000901240747, 1000000000901240749, 1000000000901240753
142: 1000000000907341867, 1000000000907341871, 1000000000907341873, 1000000000907341877, 1000000000907341879
143: 1000000000916138767, 1000000000916138771, 1000000000916138773, 1000000000916138777, 1000000000916138779
144: 1000000000918390177, 1000000000918390181, 1000000000918390183, 1000000000918390187, 1000000000918390189
145: 1000000000921370587, 1000000000921370591, 1000000000921370593, 1000000000921370597, 1000000000921370599
146: 1000000000921614851, 1000000000921614853, 1000000000921614857, 1000000000921614859, 1000000000921614863
147: 1000000000922541247, 1000000000922541251, 1000000000922541253, 1000000000922541257, 1000000000922541259
148: 1000000000927523201, 1000000000927523203, 1000000000927523207, 1000000000927523209, 1000000000927523213
149: 1000000000927612537, 1000000000927612541, 1000000000927612543, 1000000000927612547, 1000000000927612549
150: 1000000000928191091, 1000000000928191093, 1000000000928191097, 1000000000928191099, 1000000000928191103
151: 1000000000928803151, 1000000000928803153, 1000000000928803157, 1000000000928803159, 1000000000928803163
152: 1000000000939667591, 1000000000939667593, 1000000000939667597, 1000000000939667599, 1000000000939667603
153: 1000000000941123641, 1000000000941123643, 1000000000941123647, 1000000000941123649, 1000000000941123653
154: 1000000000943701181, 1000000000943701183, 1000000000943701187, 1000000000943701189, 1000000000943701193
155: 1000000000945129897, 1000000000945129901, 1000000000945129903, 1000000000945129907, 1000000000945129909
156: 1000000000945129901, 1000000000945129903, 1000000000945129907, 1000000000945129909, 1000000000945129913
157: 1000000000950642401, 1000000000950642403, 1000000000950642407, 1000000000950642409, 1000000000950642413
158: 1000000000954265947, 1000000000954265951, 1000000000954265953, 1000000000954265957, 1000000000954265959
159: 1000000000955557237, 1000000000955557241, 1000000000955557243, 1000000000955557247, 1000000000955557249
160: 1000000000960803251, 1000000000960803253, 1000000000960803257, 1000000000960803259, 1000000000960803263
161: 1000000000964893211, 1000000000964893213, 1000000000964893217, 1000000000964893219, 1000000000964893223
162: 1000000000971979867, 1000000000971979871, 1000000000971979873, 1000000000971979877, 1000000000971979879
163: 1000000000972906091, 1000000000972906093, 1000000000972906097, 1000000000972906099, 1000000000972906103
164: 1000000000973330711, 1000000000973330713, 1000000000973330717, 1000000000973330719, 1000000000973330723
165: 1000000000977937691, 1000000000977937693, 1000000000977937697, 1000000000977937699, 1000000000977937703
166: 1000000000981433857, 1000000000981433861, 1000000000981433863, 1000000000981433867, 1000000000981433869
167: 1000000000982918471, 1000000000982918473, 1000000000982918477, 1000000000982918479, 1000000000982918483
168: 1000000000985290001, 1000000000985290003, 1000000000985290007, 1000000000985290009, 1000000000985290013
用时 241.17566 秒

时空伴随者

从10^19开始的10^9个正整数内，有多少五生素数呢？
有兴趣的可以找一下其中的六生素数
2026-10-03 22:34:09
1: 10000000000011687221, 10000000000011687223, 10000000000011687227, 10000000000011687229, 10000000000011687233
2: 10000000000011763871, 10000000000011763873, 10000000000011763877, 10000000000011763879, 10000000000011763883
3: 10000000000015757021, 10000000000015757023, 10000000000015757027, 10000000000015757029, 10000000000015757033
4: 10000000000023029527, 10000000000023029531, 10000000000023029533, 10000000000023029537, 10000000000023029539
5: 10000000000026587977, 10000000000026587981, 10000000000026587983, 10000000000026587987, 10000000000026587989
6: 10000000000027727857, 10000000000027727861, 10000000000027727863, 10000000000027727867, 10000000000027727869
7: 10000000000030119971, 10000000000030119973, 10000000000030119977, 10000000000030119979, 10000000000030119983
8: 10000000000034668691, 10000000000034668693, 10000000000034668697, 10000000000034668699, 10000000000034668703
9: 10000000000035320827, 10000000000035320831, 10000000000035320833, 10000000000035320837, 10000000000035320839
10: 10000000000039891601, 10000000000039891603, 10000000000039891607, 10000000000039891609, 10000000000039891613
11: 10000000000040386867, 10000000000040386871, 10000000000040386873, 10000000000040386877, 10000000000040386879
12: 10000000000053885457, 10000000000053885461, 10000000000053885463, 10000000000053885467, 10000000000053885469
13: 10000000000063425217, 10000000000063425221, 10000000000063425223, 10000000000063425227, 10000000000063425229
14: 10000000000063466377, 10000000000063466381, 10000000000063466383, 10000000000063466387, 10000000000063466389
15: 10000000000068713771, 10000000000068713773, 10000000000068713777, 10000000000068713779, 10000000000068713783
16: 10000000000076142101, 10000000000076142103, 10000000000076142107, 10000000000076142109, 10000000000076142113
17: 10000000000092626467, 10000000000092626471, 10000000000092626473, 10000000000092626477, 10000000000092626479
18: 10000000000112742071, 10000000000112742073, 10000000000112742077, 10000000000112742079, 10000000000112742083
19: 10000000000126467337, 10000000000126467341, 10000000000126467343, 10000000000126467347, 10000000000126467349
20: 10000000000134775987, 10000000000134775991, 10000000000134775993, 10000000000134775997, 10000000000134775999
21: 10000000000139582347, 10000000000139582351, 10000000000139582353, 10000000000139582357, 10000000000139582359
22: 10000000000143313207, 10000000000143313211, 10000000000143313213, 10000000000143313217, 10000000000143313219
23: 10000000000144515457, 10000000000144515461, 10000000000144515463, 10000000000144515467, 10000000000144515469
24: 10000000000148778071, 10000000000148778073, 10000000000148778077, 10000000000148778079, 10000000000148778083
25: 10000000000156047641, 10000000000156047643, 10000000000156047647, 10000000000156047649, 10000000000156047653
26: 10000000000169987441, 10000000000169987443, 10000000000169987447, 10000000000169987449, 10000000000169987453
27: 10000000000180515967, 10000000000180515971, 10000000000180515973, 10000000000180515977, 10000000000180515979
28: 10000000000209864637, 10000000000209864641, 10000000000209864643, 10000000000209864647, 10000000000209864649
29: 10000000000219199977, 10000000000219199981, 10000000000219199983, 10000000000219199987, 10000000000219199989
30: 10000000000221150757, 10000000000221150761, 10000000000221150763, 10000000000221150767, 10000000000221150769
31: 10000000000228476097, 10000000000228476101, 10000000000228476103, 10000000000228476107, 10000000000228476109
32: 10000000000237717567, 10000000000237717571, 10000000000237717573, 10000000000237717577, 10000000000237717579
33: 10000000000239393247, 10000000000239393251, 10000000000239393253, 10000000000239393257, 10000000000239393259
34: 10000000000239927311, 10000000000239927313, 10000000000239927317, 10000000000239927319, 10000000000239927323
35: 10000000000247375347, 10000000000247375351, 10000000000247375353, 10000000000247375357, 10000000000247375359
36: 10000000000248500317, 10000000000248500321, 10000000000248500323, 10000000000248500327, 10000000000248500329
37: 10000000000255967831, 10000000000255967833, 10000000000255967837, 10000000000255967839, 10000000000255967843
38: 10000000000269566291, 10000000000269566293, 10000000000269566297, 10000000000269566299, 10000000000269566303
39: 10000000000277956841, 10000000000277956843, 10000000000277956847, 10000000000277956849, 10000000000277956853
40: 10000000000279927481, 10000000000279927483, 10000000000279927487, 10000000000279927489, 10000000000279927493
41: 10000000000281525461, 10000000000281525463, 10000000000281525467, 10000000000281525469, 10000000000281525473
42: 10000000000292629507, 10000000000292629511, 10000000000292629513, 10000000000292629517, 10000000000292629519
43: 10000000000300114151, 10000000000300114153, 10000000000300114157, 10000000000300114159, 10000000000300114163
44: 10000000000304793757, 10000000000304793761, 10000000000304793763, 10000000000304793767, 10000000000304793769
45: 10000000000323295087, 10000000000323295091, 10000000000323295093, 10000000000323295097, 10000000000323295099
46: 10000000000327880857, 10000000000327880861, 10000000000327880863, 10000000000327880867, 10000000000327880869
47: 10000000000330143821, 10000000000330143823, 10000000000330143827, 10000000000330143829, 10000000000330143833
48: 10000000000335247537, 10000000000335247541, 10000000000335247543, 10000000000335247547, 10000000000335247549
49: 10000000000342169347, 10000000000342169351, 10000000000342169353, 10000000000342169357, 10000000000342169359
50: 10000000000342855747, 10000000000342855751, 10000000000342855753, 10000000000342855757, 10000000000342855759
51: 10000000000355875327, 10000000000355875331, 10000000000355875333, 10000000000355875337, 10000000000355875339
52: 10000000000363971041, 10000000000363971043, 10000000000363971047, 10000000000363971049, 10000000000363971053
53: 10000000000366216657, 10000000000366216661, 10000000000366216663, 10000000000366216667, 10000000000366216669
54: 10000000000380773561, 10000000000380773563, 10000000000380773567, 10000000000380773569, 10000000000380773573
55: 10000000000385905331, 10000000000385905333, 10000000000385905337, 10000000000385905339, 10000000000385905343
56: 10000000000386852761, 10000000000386852763, 10000000000386852767, 10000000000386852769, 10000000000386852773
57: 10000000000393760167, 10000000000393760171, 10000000000393760173, 10000000000393760177, 10000000000393760179
58: 10000000000397150531, 10000000000397150533, 10000000000397150537, 10000000000397150539, 10000000000397150543
59: 10000000000423886351, 10000000000423886353, 10000000000423886357, 10000000000423886359, 10000000000423886363
60: 10000000000431775331, 10000000000431775333, 10000000000431775337, 10000000000431775339, 10000000000431775343
61: 10000000000440253541, 10000000000440253543, 10000000000440253547, 10000000000440253549, 10000000000440253553
62: 10000000000454133491, 10000000000454133493, 10000000000454133497, 10000000000454133499, 10000000000454133503
63: 10000000000454955851, 10000000000454955853, 10000000000454955857, 10000000000454955859, 10000000000454955863
64: 10000000000470717311, 10000000000470717313, 10000000000470717317, 10000000000470717319, 10000000000470717323
65: 10000000000471999361, 10000000000471999363, 10000000000471999367, 10000000000471999369, 10000000000471999373
66: 10000000000480112797, 10000000000480112801, 10000000000480112803, 10000000000480112807, 10000000000480112809
67: 10000000000499155721, 10000000000499155723, 10000000000499155727, 10000000000499155729, 10000000000499155733
68: 10000000000506513581, 10000000000506513583, 10000000000506513587, 10000000000506513589, 10000000000506513593
69: 10000000000510312691, 10000000000510312693, 10000000000510312697, 10000000000510312699, 10000000000510312703
70: 10000000000518624067, 10000000000518624071, 10000000000518624073, 10000000000518624077, 10000000000518624079
71: 10000000000519845727, 10000000000519845731, 10000000000519845733, 10000000000519845737, 10000000000519845739
72: 10000000000522975357, 10000000000522975361, 10000000000522975363, 10000000000522975367, 10000000000522975369
73: 10000000000524158077, 10000000000524158081, 10000000000524158083, 10000000000524158087, 10000000000524158089
74: 10000000000525023487, 10000000000525023491, 10000000000525023493, 10000000000525023497, 10000000000525023499
75: 10000000000535862761, 10000000000535862763, 10000000000535862767, 10000000000535862769, 10000000000535862773
76: 10000000000554335197, 10000000000554335201, 10000000000554335203, 10000000000554335207, 10000000000554335209
77: 10000000000572859721, 10000000000572859723, 10000000000572859727, 10000000000572859729, 10000000000572859733
78: 10000000000577052667, 10000000000577052671, 10000000000577052673, 10000000000577052677, 10000000000577052679
79: 10000000000595574787, 10000000000595574791, 10000000000595574793, 10000000000595574797, 10000000000595574799
80: 10000000000606324987, 10000000000606324991, 10000000000606324993, 10000000000606324997, 10000000000606324999
81: 10000000000609235711, 10000000000609235713, 10000000000609235717, 10000000000609235719, 10000000000609235723
82: 10000000000611166361, 10000000000611166363, 10000000000611166367, 10000000000611166369, 10000000000611166373
83: 10000000000615581367, 10000000000615581371, 10000000000615581373, 10000000000615581377, 10000000000615581379
84: 10000000000620669037, 10000000000620669041, 10000000000620669043, 10000000000620669047, 10000000000620669049
85: 10000000000633575461, 10000000000633575463, 10000000000633575467, 10000000000633575469, 10000000000633575473
86: 10000000000634241877, 10000000000634241881, 10000000000634241883, 10000000000634241887, 10000000000634241889
87: 10000000000638759817, 10000000000638759821, 10000000000638759823, 10000000000638759827, 10000000000638759829
88: 10000000000653198787, 10000000000653198791, 10000000000653198793, 10000000000653198797, 10000000000653198799
89: 10000000000655344567, 10000000000655344571, 10000000000655344573, 10000000000655344577, 10000000000655344579
90: 10000000000663165807, 10000000000663165811, 10000000000663165813, 10000000000663165817, 10000000000663165819
91: 10000000000666676171, 10000000000666676173, 10000000000666676177, 10000000000666676179, 10000000000666676183
92: 10000000000681380791, 10000000000681380793, 10000000000681380797, 10000000000681380799, 10000000000681380803
93: 10000000000682547847, 10000000000682547851, 10000000000682547853, 10000000000682547857, 10000000000682547859
94: 10000000000694662237, 10000000000694662241, 10000000000694662243, 10000000000694662247, 10000000000694662249
95: 10000000000698137531, 10000000000698137533, 10000000000698137537, 10000000000698137539, 10000000000698137543
96: 10000000000701913451, 10000000000701913453, 10000000000701913457, 10000000000701913459, 10000000000701913463
97: 10000000000711782067, 10000000000711782071, 10000000000711782073, 10000000000711782077, 10000000000711782079
98: 10000000000712583131, 10000000000712583133, 10000000000712583137, 10000000000712583139, 10000000000712583143
99: 10000000000721386541, 10000000000721386543, 10000000000721386547, 10000000000721386549, 10000000000721386553
100: 10000000000757962961, 10000000000757962963, 10000000000757962967, 10000000000757962969, 10000000000757962973
101: 10000000000780377937, 10000000000780377941, 10000000000780377943, 10000000000780377947, 10000000000780377949
102: 10000000000788698891, 10000000000788698893, 10000000000788698897, 10000000000788698899, 10000000000788698903
103: 10000000000791542377, 10000000000791542381, 10000000000791542383, 10000000000791542387, 10000000000791542389
104: 10000000000791793627, 10000000000791793631, 10000000000791793633, 10000000000791793637, 10000000000791793639
105: 10000000000793525531, 10000000000793525533, 10000000000793525537, 10000000000793525539, 10000000000793525543
106: 10000000000816183147, 10000000000816183151, 10000000000816183153, 10000000000816183157, 10000000000816183159
107: 10000000000818703691, 10000000000818703693, 10000000000818703697, 10000000000818703699, 10000000000818703703
108: 10000000000822644727, 10000000000822644731, 10000000000822644733, 10000000000822644737, 10000000000822644739
109: 10000000000826382971, 10000000000826382973, 10000000000826382977, 10000000000826382979, 10000000000826382983
110: 10000000000832175277, 10000000000832175281, 10000000000832175283, 10000000000832175287, 10000000000832175289
111: 10000000000839267821, 10000000000839267823, 10000000000839267827, 10000000000839267829, 10000000000839267833
112: 10000000000840963571, 10000000000840963573, 10000000000840963577, 10000000000840963579, 10000000000840963583
113: 10000000000871822231, 10000000000871822233, 10000000000871822237, 10000000000871822239, 10000000000871822243
114: 10000000000874186111, 10000000000874186113, 10000000000874186117, 10000000000874186119, 10000000000874186123
115: 10000000000874275361, 10000000000874275363, 10000000000874275367, 10000000000874275369, 10000000000874275373
116: 10000000000881957371, 10000000000881957373, 10000000000881957377, 10000000000881957379, 10000000000881957383
117: 10000000000885603691, 10000000000885603693, 10000000000885603697, 10000000000885603699, 10000000000885603703
118: 10000000000890092437, 10000000000890092441, 10000000000890092443, 10000000000890092447, 10000000000890092449
119: 10000000000896654097, 10000000000896654101, 10000000000896654103, 10000000000896654107, 10000000000896654109
120: 10000000000896654101, 10000000000896654103, 10000000000896654107, 10000000000896654109, 10000000000896654113
121: 10000000000906897271, 10000000000906897273, 10000000000906897277, 10000000000906897279, 10000000000906897283
122: 10000000000922752811, 10000000000922752813, 10000000000922752817, 10000000000922752819, 10000000000922752823
123: 10000000000927531867, 10000000000927531871, 10000000000927531873, 10000000000927531877, 10000000000927531879
124: 10000000000953787537, 10000000000953787541, 10000000000953787543, 10000000000953787547, 10000000000953787549
125: 10000000000959311171, 10000000000959311173, 10000000000959311177, 10000000000959311179, 10000000000959311183
126: 10000000000964111051, 10000000000964111053, 10000000000964111057, 10000000000964111059, 10000000000964111063
127: 10000000000970612021, 10000000000970612023, 10000000000970612027, 10000000000970612029, 10000000000970612033
128: 10000000000983573937, 10000000000983573941, 10000000000983573943, 10000000000983573947, 10000000000983573949
129: 10000000000984783241, 10000000000984783243, 10000000000984783247, 10000000000984783249, 10000000000984783253
130: 10000000000991099081, 10000000000991099083, 10000000000991099087, 10000000000991099089, 10000000000991099093
131: 10000000000994007701, 10000000000994007703, 10000000000994007707, 10000000000994007709, 10000000000994007713
132: 10000000000995600851, 10000000000995600853, 10000000000995600857, 10000000000995600859, 10000000000995600863
用时 652.28712 秒

yangchuanju

时空伴随者 发表于 2026-10-3 22:48
从10^19开始的10^9个正整数内，有多少五生素数呢？
有兴趣的可以找一下其中的六生素数
2026-10-03 22:34: ...

168个10^18+10^9中的最密5生素数之中有34,106,155号后加4或者35,107,156号前减4成为最密6生素数；       
132个10^19+10^9中的最密5生素数之中只有119号后加4或者120号前减4成为最密6生素数。       
编号        素数
34        1000000000210160363 is prime
35        1000000000210160347 is prime
106        1000000000675070963 is prime
107        1000000000675070947 is prime
155        1000000000945129913 is prime
156        1000000000945129897 is prime
119        10000000000896654113 is prime
120        10000000000896654097 is prime

重生888@

楼主老眼昏花，我举的是1405组四生素数，不是几个空格就能标识的

老眼昏花是事实！我的创新理论不是靠电脑水平能搜索得到的！搜到四生素数管什么用？不能当饭吃，不能为国家信息安全做贡献，那就是玩玩而已！