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Old 2021-10-09, 15:34   #1
Alex
 
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"Alex_soldier (GIMPS)"
Aug 2020
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11 Posts
Plus 4052555153018976267*2^n+1 (Pierpont 3^39*2^n+1)

Hello.
I`m working on 4052555153018976267*2^n+1 (Pierpont 3^39*2^n+1) with n=[1..10.000.000].
The range was sieved up to p=114e12.
I use Sr1sieve, PFGW, LLR.

Now it is checked n=[1..1.000.000] (49.127 of 491.804 tests).

34 small primes found:

Code:
4052555153018976267*2^2+1 is prime! (20 decimal digits)  Time : 1.235 ms.
4052555153018976267*2^11+1 is prime! (22 decimal digits)  Time : 2.454 ms.
4052555153018976267*2^82+1 is prime! (44 decimal digits)  Time : 16.804 ms.
4052555153018976267*2^100+1 is prime! (49 decimal digits)  Time : 28.723 ms.
4052555153018976267*2^106+1 is prime! (51 decimal digits)  Time : 29.094 ms.
4052555153018976267*2^131+1 is prime! (59 decimal digits)  Time : 48.247 ms.
4052555153018976267*2^160+1 is prime! (67 decimal digits)  Time : 69.903 ms.
4052555153018976267*2^310+1 is prime! (112 decimal digits)  Time : 503.097 ms.
4052555153018976267*2^490+1 is prime! (167 decimal digits)  Time : 2.631 sec.
4052555153018976267*2^1052+1 is prime! (336 decimal digits)  Time : 118.200 ms.
4052555153018976267*2^1486+1 is prime! (466 decimal digits)  Time : 44.392 ms.
4052555153018976267*2^1532+1 is prime! (480 decimal digits)  Time : 48.573 ms.
4052555153018976267*2^2995+1 is prime! (921 decimal digits)  Time : 87.253 ms.
4052555153018976267*2^4295+1 is prime! (1312 decimal digits)  Time : 67.959 ms.
4052555153018976267*2^8542+1 is prime! (2591 decimal digits)  Time : 142.527 ms.
4052555153018976267*2^10531+1 is prime! (3189 decimal digits)  Time : 183.830 ms.
4052555153018976267*2^11522+1 is prime! (3488 decimal digits)  Time : 186.658 ms.
4052555153018976267*2^19975+1 is prime! (6032 decimal digits)  Time : 465.413 ms.
4052555153018976267*2^23587+1 is prime! (7120 decimal digits)  Time : 689.028 ms.
4052555153018976267*2^25202+1 is prime! (7606 decimal digits)  Time : 751.311 ms.
4052555153018976267*2^26938+1 is prime! (8128 decimal digits)  Time : 779.696 ms.
4052555153018976267*2^28448+1 is prime! (8583 decimal digits)  Time : 929.404 ms.
4052555153018976267*2^30980+1 is prime! (9345 decimal digits)  Time : 1.017 sec.
4052555153018976267*2^48527+1 is prime! (14627 decimal digits)  Time : 2.692 sec.
4052555153018976267*2^64607+1 is prime! (19468 decimal digits)  Time : 4.952 sec.
4052555153018976267*2^251027+1 is prime! (75586 decimal digits)  Time : 81.627 sec.
4052555153018976267*2^283288+1 is prime! (85297 decimal digits)  Time : 114.207 sec.
4052555153018976267*2^313411+1 is prime! (94365 decimal digits)  Time : 126.248 sec.
4052555153018976267*2^374870+1 is prime! (112866 decimal digits)  Time : 199.486 sec.
4052555153018976267*2^446486+1 is prime! (134425 decimal digits)  Time : 303.894 sec.
4052555153018976267*2^513392+1 is prime! (154565 decimal digits)  Time : 386.964 sec.
4052555153018976267*2^648871+1 is prime! (195349 decimal digits)  Time : 570.565 sec.
4052555153018976267*2^759071+1 is prime! (228522 decimal digits)  Time : 844.726 sec.
4052555153018976267*2^903875+1 is prime! (272113 decimal digits)  Time : 1218.959 sec.
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Old 2021-10-11, 07:14   #2
bur
 
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79*6581e-4;3*2539e-3

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Interesting, I didn't know about Pierpont primes. Did you check for ((x)G))F divisibility? The chances are slim, but you never know...
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Old 2021-10-14, 09:27   #3
Alex
 
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Aug 2020
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Hello, bur.

I myself accidentally found out about Pierpont primes looking someone's old results page.

3^39 is max < 2^63.

When I discovered a new Proth prime (P), I check a lot of possible chains and numbers near it:

Code:
F() & GF() & xGF() // Possible Fermat divisor
P+2 // Possible Twins
P-2 // Possible Twins
P+4 // Possible Cousins
P-4 // Possible Cousins
P+6 // Possible Sexy or part of AP
P-6 // Possible Sexy or part of AP
P+8 // Possible part of tuplet
P-8 // Possible part of tuplet
P+10 // Possible part of tuplet
P-10 // Possible part of tuplet
P+12 // Possible part of AP
P-12 // Possible part of AP
P+18 // Possible part of AP
P-18 // Possible part of AP
P+24 // Possible part of AP
P-24 // Possible part of AP
P+30 // Possible part of AP
P-30 // Possible part of AP
P+210 // Possible part of AP
P-210 // Possible part of AP
2*P+1 // Possible Cunningham 1st or Safe / Sophie Germain
2*P-1 // Possible Cunningham 2nd
(P+1)/2 // Possible Cunningham 2nd
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Old 2021-10-14, 15:21   #4
dannyridel
 
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Jan 2020
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Quote:
Originally Posted by Alex View Post
Hello.
I`m working on 4052555153018976267*2^n+1 (Pierpont 3^39*2^n+1) with n=[1..10.000.000].
The range was sieved up to p=114e12.
I use Sr1sieve, PFGW, LLR.

Now it is checked n=[1..1.000.000] (49.127 of 491.804 tests).

34 small primes found:

Code:
4052555153018976267*2^2+1 is prime! (20 decimal digits)  Time : 1.235 ms.
4052555153018976267*2^11+1 is prime! (22 decimal digits)  Time : 2.454 ms.
4052555153018976267*2^82+1 is prime! (44 decimal digits)  Time : 16.804 ms.
4052555153018976267*2^100+1 is prime! (49 decimal digits)  Time : 28.723 ms.
4052555153018976267*2^106+1 is prime! (51 decimal digits)  Time : 29.094 ms.
4052555153018976267*2^131+1 is prime! (59 decimal digits)  Time : 48.247 ms.
4052555153018976267*2^160+1 is prime! (67 decimal digits)  Time : 69.903 ms.
4052555153018976267*2^310+1 is prime! (112 decimal digits)  Time : 503.097 ms.
4052555153018976267*2^490+1 is prime! (167 decimal digits)  Time : 2.631 sec.
4052555153018976267*2^1052+1 is prime! (336 decimal digits)  Time : 118.200 ms.
4052555153018976267*2^1486+1 is prime! (466 decimal digits)  Time : 44.392 ms.
4052555153018976267*2^1532+1 is prime! (480 decimal digits)  Time : 48.573 ms.
4052555153018976267*2^2995+1 is prime! (921 decimal digits)  Time : 87.253 ms.
4052555153018976267*2^4295+1 is prime! (1312 decimal digits)  Time : 67.959 ms.
4052555153018976267*2^8542+1 is prime! (2591 decimal digits)  Time : 142.527 ms.
4052555153018976267*2^10531+1 is prime! (3189 decimal digits)  Time : 183.830 ms.
4052555153018976267*2^11522+1 is prime! (3488 decimal digits)  Time : 186.658 ms.
4052555153018976267*2^19975+1 is prime! (6032 decimal digits)  Time : 465.413 ms.
4052555153018976267*2^23587+1 is prime! (7120 decimal digits)  Time : 689.028 ms.
4052555153018976267*2^25202+1 is prime! (7606 decimal digits)  Time : 751.311 ms.
4052555153018976267*2^26938+1 is prime! (8128 decimal digits)  Time : 779.696 ms.
4052555153018976267*2^28448+1 is prime! (8583 decimal digits)  Time : 929.404 ms.
4052555153018976267*2^30980+1 is prime! (9345 decimal digits)  Time : 1.017 sec.
4052555153018976267*2^48527+1 is prime! (14627 decimal digits)  Time : 2.692 sec.
4052555153018976267*2^64607+1 is prime! (19468 decimal digits)  Time : 4.952 sec.
4052555153018976267*2^251027+1 is prime! (75586 decimal digits)  Time : 81.627 sec.
4052555153018976267*2^283288+1 is prime! (85297 decimal digits)  Time : 114.207 sec.
4052555153018976267*2^313411+1 is prime! (94365 decimal digits)  Time : 126.248 sec.
4052555153018976267*2^374870+1 is prime! (112866 decimal digits)  Time : 199.486 sec.
4052555153018976267*2^446486+1 is prime! (134425 decimal digits)  Time : 303.894 sec.
4052555153018976267*2^513392+1 is prime! (154565 decimal digits)  Time : 386.964 sec.
4052555153018976267*2^648871+1 is prime! (195349 decimal digits)  Time : 570.565 sec.
4052555153018976267*2^759071+1 is prime! (228522 decimal digits)  Time : 844.726 sec.
4052555153018976267*2^903875+1 is prime! (272113 decimal digits)  Time : 1218.959 sec.
The first two aren't proth primes, just fyi.
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Old 2021-10-15, 10:16   #5
Alex
 
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Quote:
Originally Posted by dannyridel View Post
The first two aren't proth primes, just fyi.
Sure. So there is no word "proth" in the first post.
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Old 2021-10-16, 04:15   #6
dannyridel
 
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Jan 2020
Bellevue, WA

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Yep. Any new primes?
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