20201126, 01:01  #1 
Nov 2020
1 Posts 
Help? I have been holding on to a Prime
Yes, I have been holding on to a Prime I generated in 2011 by reverse engineering an RSA algorithm. The suspected Prime is over 26 million digits. I have been trying to factor it since discovery. Unsuccessful attempts have been made and i did have my Mathematics professor take a look at it and by using some type of modular mathematics found it probable by looking at the first and last digit. If there is anyone who can help me please contact me. Thanks!
Gary 
20201126, 01:27  #2  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,663 Posts 
Quote:
Tell us more! 

20201126, 02:16  #3  
Feb 2017
Nowhere
2^{2}·13·83 Posts 
Quote:
Quote:
There is a way to tell a number greater than ten is composite by its last decimal digit alone  if that digit is 2, 4, 5, 6, 8, or 0, the number is composite. Last fiddled with by Dr Sardonicus on 20201126 at 02:17 Reason: gixnif stopy 

20201126, 04:01  #4  
May 2020
35_{8} Posts 
Quote:
There are no promises on it being particularly quick  if you dedicate a desktop computer to it, I'm fairly certain it'll finish in a year? Couple months? I really don't know the timescale for PRP tests on big numbers like that At the very least, if it's a probable prime, it will let you know there's a very good chance it's prime  and, if the form of the number is conducive to it, may even let you absolutely prove it's primality. Would check if it's "probably" prime first, though. 

20201126, 06:10  #5  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
11451_{8} Posts 
Quote:
(It would in any event be smaller than the smallest (LL or PRP)untested Mersenne number, at ~86.4Mbits vs. ~98.6Mbits at the moment.) A similar sized Mersenne number can be primality tested in about a day on a Radeon VII gpu. A number of that size, not of a special form, may be entirely untestable in a human lifespan. If I understand correctly, the current record for pfgw is 2.56 Megadigits. The run time scaling for LL or PRP based primality testing with the best software for testing Mersennes is ~p^{2.1} where p is the exponent of the Mersenne number (due mainly to run time of the irrational base discrete weighted transform squaring operations and ~p iterations required), so 26. megadigits would be more than 100 times more effort than the current pfgw record, and would be remarkable / incredible for 2011 or now. What specific factoring has been applied to the suspected prime? Why is it suspected to be prime? First and last digit only makes little or no indication of primality. A few examples: 11 prime 121 composite 131 prime 1331 composite 1151 prime 11511 composite Disclose the form of the number here if you know it, and people may be able to advise how best to attack it. Last fiddled with by kriesel on 20201126 at 07:03 

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