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 2021-02-01, 09:43 #243 kar_bon     Mar 2006 Germany 295110 Posts base 738 (738^15864-1)^2-2 is prime, 90998 digits pfgw64 -tp -q"(738^15864-1)^2-2" PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8] Primality testing (738^15864-1)^2-2 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) (738^15864-1)^2-2 is prime! (534.4768s+0.1565s) For this base there was no prime on the -1 side up to n=10k. Primes so far, tested to n=25k: -1: 15864 +1: 3, 18, 5892 No further reservation. Stats: 82 bases < 3000 with no Carol prime.
 2021-03-02, 08:52 #244 kar_bon     Mar 2006 Germany 13·227 Posts Base 938 Another one down: Base 938 tested to n=22k Found primes so far: -1: 21852 +1: 54, 56, 654, 749, 3916, 11463 No further reservation. (938^21852-1)^2-2 has 129898 digits
 2021-03-25, 01:24 #245 Dylan14     "Dylan" Mar 2017 11178 Posts Base 832 complete to n = 25k. Seven primes found: Code: (832^26+1)^2-2 (832^51+1)^2-2 (832^62+1)^2-2 (832^5882+1)^2-2 (832^7795+1)^2-2 (832^8375+1)^2-2 (832^18830+1)^2-2 All but the last prime on the list was found by kar_bon, noted here: https://www.rieselprime.de/ziki/Carol-Kynea_prime_832 A Carol prime for this base remains elusive...
 2021-04-05, 20:39 #246 kuratkull     Mar 2007 Estonia 149 Posts Base 42 tested to n=100k (continuing) Two primes found: Code: (42^33475+1)^2-2 is 3-PRP! (135.6747s+0.0009s) (42^40891-1)^2-2 is 3-PRP! (199.4855s+0.0010s)
 2021-05-06, 10:57 #247 kar_bon     Mar 2006 Germany B8716 Posts b=832 Searched to n=52k and found: PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8] Primality testing (832^51686-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 23, base 1+sqrt(23) Running N+1 test using discriminant 23, base 2+sqrt(23) (832^51686-1)^2-2 is prime! (13534.9333s+0.1916s) 301859 digits, so no Top5000 entry. Another Carol-absence-base has fallen.
2021-05-07, 01:54   #248
gd_barnes

May 2007
Kansas; USA

22×52×107 Posts

Quote:
 Originally Posted by kar_bon Searched to n=52k and found: PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8] Primality testing (832^51686-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 23, base 1+sqrt(23) Running N+1 test using discriminant 23, base 2+sqrt(23) (832^51686-1)^2-2 is prime! (13534.9333s+0.1916s) 301859 digits, so no Top5000 entry. Another Carol-absence-base has fallen.
Very good! I assume that you searched both Carol and Kynea to n=52k. I also assume that you are releasing this base. Is that correct?

Last fiddled with by gd_barnes on 2021-05-07 at 01:54

 2021-05-08, 06:55 #249 kar_bon     Mar 2006 Germany 295110 Posts As usual I always search both sides together and no further reservation on this base.
 2021-05-19, 12:14 #250 rogue     "Mark" Apr 2003 Between here and the 11·599 Posts (1534^2147+1)^2-2 (1534^2665+1)^2-2 (1540^4484-1)^2-2 (1542^5825+1)^2-2 (1542^6888+1)^2-2 (1566^8188-1)^2-2 (1570^2310+1)^2-2 (1614^2907+1)^2-2 (1650^3219-1)^2-2 (1684^5605+1)^2-2 (1706^8028-1)^2-2 (1726^4221+1)^2-2 (1760^6210+1)^2-2 (1774^2061-1)^2-2 (1774^2249+1)^2-2 (1806^3666-1)^2-2 (1806^8128-1)^2-2 (1806^9942-1)^2-2 (1928^4650-1)^2-2 (1928^4870+1)^2-2 (1950^8442+1)^2-2 (1986^3738+1)^2-2 (2064^2698-1)^2-2 (2076^2217+1)^2-2 (2076^6182-1)^2-2 (2104^2741-1)^2-2 (2140^3857-1)^2-2 (2146^7710-1)^2-2 (2266^5906+1)^2-2 (2280^2590-1)^2-2 (2280^3443-1)^2-2 (2290^4114+1)^2-2 (2312^4671-1)^2-2 (2312^4887-1)^2-2 (2342^4232-1)^2-2 (2382^2498+1)^2-2 (2382^4175+1)^2-2 (2384^3411+1)^2-2 (2384^7398-1)^2-2 (2398^5485+1)^2-2 (2400^3148-1)^2-2 (2400^4589+1)^2-2 (2400^7021+1)^2-2 (2400^9993+1)^2-2 (2404^2828-1)^2-2 (2474^8041-1)^2-2 (2524^2208+1)^2-2 (2524^3272-1)^2-2 (2574^2280-1)^2-2 (2610^5581-1)^2-2 (2610^7874-1)^2-2 (2614^3383+1)^2-2 (2616^2457+1)^2-2 (2616^8123-1)^2-2 (2622^6882-1)^2-2 (2624^2702+1)^2-2 (2626^4436+1)^2-2 (2650^9393-1)^2-2 (2658^2548-1)^2-2 (2660^3979+1)^2-2 (2846^8189-1)^2-2 (2886^7330-1)^2-2 (2904^3400+1)^2-2 (2944^5817-1)^2-2 (2970^2993+1)^2-2 are all prime.
 2021-08-30, 08:08 #251 kuratkull     Mar 2007 Estonia 149 Posts Code: (42^106238+1)^2-2 is 3-PRP!
 2021-09-13, 07:59 #252 kar_bon     Mar 2006 Germany 13×227 Posts CK 688 (688^85121+1)^2-2 is prime (483077 digits, ~4000 digits too small for Top5000) PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8] Primality testing (688^85121+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) (688^85121+1)^2-2 is prime! (40126.3937s+0.0126s) Tested both sides to n=85700, continuing.
 2021-10-01, 10:04 #253 kuratkull     Mar 2007 Estonia 149 Posts (42^157323+1)^2-2 is prime! Digits:510749 Barely got into Top5K at position 4286, it was estimated that it'll drop out in about 10 weeks time. https://primes.utm.edu/primes/page.php?id=132772

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