 mersenneforum.org 4052555153018976267*2^n+1 (Pierpont 3^39*2^n+1)
 Register FAQ Search Today's Posts Mark Forums Read 2021-10-09, 15:34 #1 Alex   "Alex_soldier (GIMPS)" Aug 2020 www.Mersenne.ru 11 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 13·31 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 1110 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

23·7 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

B16 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 23·7 Posts Yep. Any new primes?  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post science_man_88 science_man_88 0 2018-02-21 03:02

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