View Single Post
Old 2020-05-17, 18:02   #4
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

14210 Posts
Thumbs up

Quote:
Originally Posted by kruoli View Post
2^11214-3 has a factor: 1796673824281091446021443177301
2^21702-3 has a factor: 22313687645759
Impressive. Can they be guaranteed to be minimal?

Only one composite without known factor, and one for which it is not known if it is prime or not. Updating:
Code:
        p:  factor of 2^{p+1} - 3
----------------------------------
        2:  prime
        3:  prime
        5:  prime
        7:  11
       13:  prime
       17:  11
       19:  prime
       31:  9241
       61:  37
       89:  1823
      107:  11
      127:  11
      521:  193
      607:  11
     1279:  98807
     2203:  47
     2281:  131
     3217:  11
     4253:  23
     4423:  313
     9689:  289935200473
     9941:  419303
    11213:  1796673824281091446021443177301
    19937:  11
    21701:  22313687645759
    23209:  37
    44497:  11
    86243:  6553
   110503:  313
   132049:  composite
   216091:  23
   756839:  757
   859433:  193
  1257787:  11
  1398269:  96997
  2976221:  1451
  3021377:  11
  6972593:  103869349
 13466917:  11
 20996011:  86183
 24036583:  59
 25964951:  76382783
 30402457:  11
 32582657:  11
 37156667:  11
 42643801:  38334482051
 43112609:  59
 57885161:  193
 74207281:  unknown!
 77232917:  11
 82589933:  37463
/JeppeSN

Last fiddled with by JeppeSN on 2020-05-17 at 18:03
JeppeSN is offline   Reply With Quote