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发表于 2026-9-5 06:09
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本帖最后由 yangchuanju 于 2026-9-5 15:02 编辑
2021年4月16日愚公(奚)老师在花费近几天几夜的时间后,计算出2的41-50次方的哥猜素数对数(仅2的50次方就花费37个多小时),
首次发布在yangchuanju的帖子《实用哥猜数表》27楼上,现转载如下——
http://www.mathchina.com/bbs/for ... B5%D3%C3&page=3
G(2^41)= 1934814452,
G(2^42)= 3680759328,
G(2^43)= 7010898161,
G(2^44)= 13369466800,
G(2^45)= G(35184372088832)=25,522,944,188 ,
G(2^46)= G(70368744177664) = 48776696083 ,
G(2^47)= G(140,737,488,355,328) = 93,311,971,184,(time use 11658.95 sec )~3.238h,
G(2^48)= G( 281474976710656 ) = 178680063951 , (time use 27491.85 sec )~7.64h
G(2^49)= G( 562949953421312 ) = 342469661688;  (time use ? sec )
G(2^50)= G(1125899906842624)= 656978437719 (133767.06 sec)=37h 9'27"
比2^50更大的偶数素对数量的筛选太费时了,不筛选了。
亦即2^41--2^50单计哥猜素数对数分别是——
指数 幂数 素数对数
41 2199023255552 1934814452
42 4398046511104 3680759328
43 8796093022208 7010898161
44 17592186044416 13369466800
45 35184372088832 25522944188
46 70368744177664 48776696083
47 140737488355328 93311971184
48 281474976710656 178680063951
49 562949953421312 342469661688
50 1125899906842624 656978437719
奚老师完全可以向OEIS网站申报,接续在A006307之后,将A006307扩展到2^50!
A006307
Number of ways writing 2^n as unordered sums of 2 primes.
0 0
1 0
2 1
3 1
4 2
5 2
6 5
7 3
8 8
9 11
10 22
11 25
12 53
13 76
14 151
15 244
16 435
17 749
18 1314
19 2367
20 4239
21 7471
22 13705
23 24928
24 45746
25 83467
26 153850
27 283746
28 525236
29 975685
30 1817111
31 3390038
32 6341424
33 11891654
34 22336060
35 42034097
36 79287664
37 149711134
38 283277225
39 536710100
40 1018369893
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