mersenneforum.org Code for testing a prime other than form 2^n-1
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 2013-04-18, 05:34 #1 MercPrime     Jan 2009 1/n 258 Posts Code for testing a prime other than form 2^n-1 Hello, I thought there was a guide to entering a line in the worktodo file, but I searched and cant seem to find it. I have a candidate for a Sophia Prime of form 2^n +1 or there abouts (small number, nothing huge) and was looking to do a quick test. So is there a way to specify the form, or would I have to crunch the numbers to come up with an exponent that has decimals or something. Thanks!
 2013-04-18, 11:59 #2 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 17·251 Posts http://www.mersenneforum.org/showpos...33&postcount=6 shows the worktodo line formats. If you're trying to do something that's not supported by Prime95, check out PFGW or LLR. Last fiddled with by Mini-Geek on 2013-04-18 at 12:00
2013-04-18, 17:37   #3
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×3,041 Posts

Quote:
 Originally Posted by MercPrime ...I have a candidate for a Sophia Prime of form 2^n +1 ...
All 2^n+1 numbers (except n=2m) are composite, in case you were unsure.

 2013-04-19, 03:20 #4 MercPrime     Jan 2009 1/n 3×7 Posts Thank you Mini-Geek and Batalov, been a while so I have to dust off the brain a little!
 2013-05-12, 18:35 #5 Unregistered   7·1,117 Posts Mersenne Primes The point of the program is that there is a special method to find primes which CAN be expressed as (2^P)-1. There are definitely some prime numbers expressed as (2^P)+1 (I think for certain even P's...) but those numbers cannot use the Lucas Lehmer algorithm. The algorithm was specially designed for Mersenne primes only. It saves an enormous amount of time over other conventional primality tests which is why all the biggest primes discovered to date are Mersenne primes. I couldn't explain the proof of the Lucas Lehmer test if I tried, but I do know it takes advantage of the fact that the binary form of a mersenne number is 111.........111, whereas your proposed candidate is 1000.........0001.
2013-05-12, 22:03   #6

"Richard B. Woods"
Aug 2002
Wisconsin USA

718810 Posts

Quote:
 Originally Posted by Unregistered There are definitely some prime numbers expressed as (2^P)+1 (I think for certain even P's...)
... but, as pointed out above, only if P = 2m.

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