Carol / Kynea Primes - Page 23

kar_bon · 2021-02-01, 09:43

(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.

kar_bon · 2021-03-02, 08:52

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

Dylan14 · 2021-03-25, 01:24

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...

kuratkull · 2021-04-05, 20:39

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)

kar_bon · 2021-05-06, 10:57

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.

gd_barnes · 2021-05-07, 01:54

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?

kar_bon · 2021-05-08, 06:55

As usual I always search both sides together and no further reservation on this base.

rogue · 2021-05-19, 12:14

(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.

kuratkull · 2021-08-30, 08:08

Code:

(42^106238+1)^2-2 is 3-PRP!

kar_bon · 2021-09-13, 07:59

(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.

kuratkull · 2021-10-01, 10:04

(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

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.

2021-05-08, 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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