素数求证题

cz1

太阳

yangchuanju 发表于 2023-6-14 19:49
太阳1楼第一求证题：
已知：整数a>0,  c>10,  h>0,  m>0,  t>0
a^c-a=mt,  c=2k,  (m+1)/k=h,  素数k>0,  ...

找到一个反例m是偶数，如果m取奇数，命题应该是正确的

Treenewbee

已知整数m>0,素数y>0,求证m=y?

Treenewbee

\[2^{2*47}-2=15032385529*1317624577307106158\]
\[15032385529+1=47*319837990\]
\[15032385529=7* 2147483647\]

Treenewbee

{23, {1057, 33287012383}}

Treenewbee

{41, {348026566111, 6947319183841}},
{47, {15032385529,   658812288653553079}}

Treenewbee

{53, {27559, 75047, 904921, 53020457, 200342119, 427642159,
  141541043689, 178256365343, 385435999337, 579359984591,
  1141614405743, 3108775220719, 37485788659217, 2196339399480289,
  18469285401382879, 1082138609276112143, 13048488979502827249,
  35532855054419560817, 70016605023110341841, 105243981561348967463,
  227564491900464368417, 286594037673157805479,
  94856922671422910031409, 202477738629206277127849,
  765078641387480701041383, 44826917716909366505909911,
  540525526767270388528448873, 1471926383660631403457836009}}

Treenewbee

{59, {37791151, 994133479, 30083996115310921, 5522986335866214151, 167133994562026498368209449,
  4396624476272619590574943921}},
{71, {46425161116741073,   60044878310850109287265487}},
{79, {1409477752912188912089, 129613755370670536325087639}},
{83, {143998193, 264464696783,   46505423295079, 1005647278981711443585267111433950889,
  176840436411682078246734480505964994257,   324782217194828919710943280009916906589167}},
{89, {11606006073454350334822367, 16505414644438543076808428513}}

Treenewbee

太阳1楼第2求证题反例：

{43, {369269551}},
{53, {2275183, 14822523673}},
{61, {9271, 1531366081, 142123242012031}},
{67, {3307331370614831}},
{73, {12089912018588257}},
{97, {89580746449, 6578503584841, 13763992111142401, 1010780497307234809}}

yangchuanju

太阳 发表于 2023-6-14 22:27
找到一个反例m是偶数，如果m取奇数，命题应该是正确的

太阳先生不是热衷于研究大素数吗？
下面是第45,46,47号清一色数的唯一φ因子，分别有1001位，1031位，1128位：
45  10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000099999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001——1001位，对应清一色数是R3750

46  11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111——1031位，对应清一色数是R1031

47  999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990001——1128位，对应清一色数是R2262