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 2021-10-09, 15:34 #1 Alex     "Alex_soldier (GIMPS)" Aug 2020 www.Mersenne.ru 1510 Posts 4052555153018976267*2^n+1 (Pierpont 3^39*2^n+1) Hello. Im 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.
 2021-10-11, 07:14 #2 bur     Aug 2020 79*6581e-4;3*2539e-3 2×211 Posts Interesting, I didn't know about Pierpont primes. Did you check for ((x)G))F divisibility? The chances are slim, but you never know...
 2021-10-14, 09:27 #3 Alex     "Alex_soldier (GIMPS)" Aug 2020 www.Mersenne.ru 3·5 Posts 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
2021-10-14, 15:21   #4
dannyridel

"AMD YES!"
Jan 2020
Bellevue, WA

4116 Posts

Quote:
 Originally Posted by Alex Hello. Im 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.

2021-10-15, 10:16   #5
Alex

"Alex_soldier (GIMPS)"
Aug 2020
www.Mersenne.ru

178 Posts

Quote:
 Originally Posted by dannyridel The first two aren't proth primes, just fyi.
Sure. So there is no word "proth" in the first post.

 2021-10-16, 04:15 #6 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 5×13 Posts Yep. Any new primes?
2021-10-31, 13:32   #7
Alex

"Alex_soldier (GIMPS)"
Aug 2020
www.Mersenne.ru

3×5 Posts

Quote:
 Originally Posted by dannyridel Yep. Any new primes?
I have 8 active projects now (AP, xGF, Mersenne GPU TF, Near-repdigit, Proth, Pierpont, SG)
and report news in suitable thread, when pass a milestone or discover a new prime.
So see you soon