Thread: Factorize a 129-digit number View Single Post
2021-04-09, 22:50   #9
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

1000000011112 Posts

Quote:
 Originally Posted by a1call Code: 33765749444723236975938383549571694531728722961303548619829414070181324100^2+1 = 6811381392746490569 x 167385405371362584782846408982573842467658758597134437038484622185119073107121016763971211022426995195588062521818021967340171529 I have no idea how frmky could have figured that out or what the significance of any of the numbers are. ETA: PARI-GP code: Code: factor(6811381392746490569 ) %8 = [ 109 1] [ 23917 1] [2612774911073 1] ETA II One thing you can be sure of is that none of the prime factors p of OP-Number will be of the form 2n+1 where n is an odd integer, so you can rule out the infinite set 3, 7, 11,19, ....as candidates
ETA III You can also be sure that at least one of the prime factors of OP-Number will be of the form 4*n+1 where n is an odd integer.