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 ET_ 2013-02-15 19:58

Proth primes

While working on GFNs (N=6000-6150, k=50,000,000-2,500,00,000), Markus Tervoonen gathered a huge list of Proth primes (about 40 millions).

Luigi

 ATH 2019-05-18 05:48

Starting Proth prime test of 123173*2^333333+1
Using all-complex FMA3 FFT length 30K, Pass1=640, Pass2=48, clm=2, a = 3
[B]123173*2^333333+1 is prime![/B] (100349 decimal digits) Time : 46.491 sec.

Starting Proth prime test of 182931*2^333333+1
Using all-complex FMA3 FFT length 30K, Pass1=640, Pass2=48, clm=2, a = 5
[B]182931*2^333333+1 is prime![/B] (100349 decimal digits) Time : 46.459 sec.

Starting Proth prime test of 1460231*2^333333+1
Using zero-padded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 3
[B]1460231*2^333333+1 is prime![/B] (100350 decimal digits) Time : 49.041 sec.

Starting Proth prime test of 1569345*2^333333+1
Using zero-padded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 11
[B]1569345*2^333333+1 is prime![/B] (100350 decimal digits) Time : 49.245 sec.

Starting Proth prime test of 1714923*2^333333+1
Using zero-padded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 5
[B]1714923*2^333333+1 is prime![/B] (100350 decimal digits) Time : 48.322 sec.

Starting Proth prime test of 1751013*2^333333+1
Using zero-padded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 5
[B]1751013*2^333333+1 is prime![/B] (100350 decimal digits) Time : 49.114 sec.

Starting Proth prime test of 1852761*2^333333+1
Using zero-padded FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2, a = 5
[B]1852761*2^333333+1 is prime![/B] (100350 decimal digits) Time : 49.546 sec.

 Chara34122 2019-07-31 06:05

I'm interested. Besides, today I've found one: 305147*2^1030527+1 (310226 digits long) from [url]http://irvinemclean.com/maths/sierpin3.htm[/url] . How can I check it for being a Fermat, GF, xGF divisor?

 Dylan14 2019-07-31 12:23

[QUOTE=Chara34122;522691]I'm interested. Besides, today I've found one: 305147*2^1030527+1 (310226 digits long) from [url]http://irvinemclean.com/maths/sierpin3.htm[/url] . How can I check it for being a Fermat, GF, xGF divisor?[/QUOTE]

You could use pfgw to test the number for Fermat divisibility. You’ll want to use the -gxo flag (which does the tests without testing to see if the number is prime). An appropriate command line for Windows would be

[CODE]pfgw64 -gxo -q”305147*2^1030527+1”[/CODE]

 Chara34122 2019-08-28 17:47

If anyone is interested : one more 285473*2^530921+1 is prime! (159829 decimal digits).

 rudy235 2019-09-09 23:17

A new prime has been discovered (pending verification) and has 5,269,954 digits.

It is 7 ·6[SUP] 6772401[/SUP] + 1 .

Although I am doubtful it was checked as a Proth Prime, it might be represented as such

[STRIKE][7*3**6772401* 2**6772401 +1 .[/STRIKE] [URL="https://primes.utm.edu/primes/page.php?id=129914"]https://primes.utm.edu/primes/page.php?id=129914[/URL]

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[SUP]n[/SUP] N=[I]k[/I]2[SUP]n[/SUP]+1 so I ammend my previous statement.

 pepi37 2019-09-11 09:23

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.

 ixfd64 2019-09-17 16:45

I imagine he still does.

 storm5510 2020-02-15 16:06

[QUOTE=rudy235;525594]...A Proth number is restricted to k k>2[SUP]n[/SUP] N=[I]k[/I]2[SUP]n[/SUP]+1 so I ammend my previous statement.[/QUOTE]

Would the simple form of this not be k*2^n+1?

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