20130215, 19:58  #1 
Banned
"Luigi"
Aug 2002
Team Italia
1001011111011_{2} Posts 
Proth primes
While working on GFNs (N=60006150, k=50,000,0002,500,00,000), Markus Tervoonen gathered a huge list of Proth primes (about 40 millions).
If you are interested please leave a message... Luigi 
20190518, 05:48  #2 
Einyen
Dec 2003
Denmark
3^{2}×383 Posts 
Starting Proth prime test of 123173*2^333333+1
Using allcomplex FMA3 FFT length 30K, Pass1=640, Pass2=48, clm=2, a = 3 123173*2^333333+1 is prime! (100349 decimal digits) Time : 46.491 sec. Starting Proth prime test of 182931*2^333333+1 Using allcomplex FMA3 FFT length 30K, Pass1=640, Pass2=48, clm=2, a = 5 182931*2^333333+1 is prime! (100349 decimal digits) Time : 46.459 sec. Starting Proth prime test of 1460231*2^333333+1 Using zeropadded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 3 1460231*2^333333+1 is prime! (100350 decimal digits) Time : 49.041 sec. Starting Proth prime test of 1569345*2^333333+1 Using zeropadded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 11 1569345*2^333333+1 is prime! (100350 decimal digits) Time : 49.245 sec. Starting Proth prime test of 1714923*2^333333+1 Using zeropadded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 5 1714923*2^333333+1 is prime! (100350 decimal digits) Time : 48.322 sec. Starting Proth prime test of 1751013*2^333333+1 Using zeropadded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 5 1751013*2^333333+1 is prime! (100350 decimal digits) Time : 49.114 sec. Starting Proth prime test of 1852761*2^333333+1 Using zeropadded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 5 1852761*2^333333+1 is prime! (100350 decimal digits) Time : 49.546 sec. Last fiddled with by ATH on 20190519 at 16:49 
20190731, 06:05  #3 
Nov 2018
Russia
111_{2} Posts 
I'm interested. Besides, today I've found one: 305147*2^1030527+1 (310226 digits long) from http://irvinemclean.com/maths/sierpin3.htm . How can I check it for being a Fermat, GF, xGF divisor?

20190731, 12:23  #4  
"Dylan"
Mar 2017
3×199 Posts 
Quote:
Code:
pfgw64 gxo q”305147*2^1030527+1” 

20190828, 17:47  #5 
Nov 2018
Russia
7 Posts 
If anyone is interested : one more 285473*2^530921+1 is prime! (159829 decimal digits).

20190909, 23:17  #6 
Jun 2015
Vallejo, CA/.
1155_{10} Posts 
A new prime has been discovered (pending verification) and has 5,269,954 digits.
It is 7 ·6^{ 6772401} + 1 . Although I am doubtful it was checked as a Proth Prime, it might be represented as such It is by far the largest Prime of 2019 and if verified it will rank as #18 in the list of Largest Primes kept by CC Congratulations to Ryan Propper. Edit: A Proth number is restricted to k k>2^{n} N=k2^{n}+1 so I ammend my previous statement. Last fiddled with by rudy235 on 20190910 at 00:15 
20190911, 09:23  #7 
Dec 2011
After milion nines:)
2×3^{2}×7×13 Posts 
Congratulations to Ryan Propper.
He really earn this prime: but I cannot even imagine what resources he has. If we make initial sieve , then assume sieve depth, from last prime we have at least 100000 candidates from 2.8M digits and above :) And he process 100000 those candidates in 34 days. Some supercomputer must be behind scene. 
20190917, 16:45  #8 
Bemusing Prompter
"Danny"
Dec 2002
California
4704_{8} Posts 
He mentioned a few years ago that he had access to a cluster: https://mersenneforum.org/showthread.php?t=17690
I imagine he still does. 
20200215, 16:06  #9 
Random Account
Aug 2009
Not U. + S.A.
2×3×19×23 Posts 

20201002, 07:11  #10 
Sep 2002
Database er0rr
5·911 Posts 

20211202, 07:28  #11 
Jun 2015
Vallejo, CA/.
3×5×7×11 Posts 
Largest Prime in 3 Years. 6.4 Million Digits
If confirmed it will be the largest since Dec 2018
13 202705 · 2^{21320516} + 1 6418121 L5181 Dec 2021 (Unverified because InProcess) Congratulations to Pavel Atnashev and PrimeGrid Moderator note: Moved from Riesel prime thread, parked here for now. Last fiddled with by Dr Sardonicus on 20211202 at 13:22 
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