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Message boards : Wieferich and Wall-Sun-Sun Prime Search : WSS with A = -1 found!

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Joined: 25 Feb 20
Posts: 514
ID: 1241833
Credit: 412,255,445
RAC: 18,902
321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,315,295)ESP LLR Ruby: Earned 2,000,000 credits (2,151,088)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,620,968)PPS LLR Jade: Earned 10,000,000 credits (15,382,679)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Ruby: Earned 2,000,000 credits (2,434,466)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Ruby: Earned 2,000,000 credits (2,027,649)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Turquoise: Earned 5,000,000 credits (5,096,952)AP 26/27 Turquoise: Earned 5,000,000 credits (5,797,662)GFN Jade: Earned 10,000,000 credits (10,874,159)WW Double Silver: Earned 200,000,000 credits (349,980,000)PSA Amethyst: Earned 1,000,000 credits (1,042,601)
Message 151403 - Posted: 6 Sep 2021 | 6:40:28 UTC

7665762181374748069

found by GregCinAZ is a Wall-Sun-Sun prime with A = -1.

I couldn't find a list of near WSS primes, impressive nontheless.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

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titoProject donor
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Joined: 28 Jun 08
Posts: 2
ID: 24708
Credit: 1,029,599,100
RAC: 2,643
321 LLR Amethyst: Earned 1,000,000 credits (1,307,323)Cullen LLR Gold: Earned 500,000 credits (590,131)ESP LLR Amethyst: Earned 1,000,000 credits (1,106,344)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (121,358)PPS LLR Amethyst: Earned 1,000,000 credits (1,468,028)PSP LLR Amethyst: Earned 1,000,000 credits (1,093,233)SoB LLR Ruby: Earned 2,000,000 credits (2,019,301)SR5 LLR Gold: Earned 500,000 credits (607,747)SGS LLR Ruby: Earned 2,000,000 credits (2,052,314)TRP LLR Gold: Earned 500,000 credits (646,994)Woodall LLR Gold: Earned 500,000 credits (618,819)321 Sieve (suspended) Gold: Earned 500,000 credits (787,608)Cullen/Woodall Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,322,072)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,114,520)PPS Sieve Double Silver: Earned 200,000,000 credits (234,743,238)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (101,938)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,209,597)AP 26/27 Sapphire: Earned 20,000,000 credits (26,999,713)GFN Double Bronze: Earned 100,000,000 credits (103,724,946)WW Double Gold: Earned 500,000,000 credits (500,184,000)PSA Double Bronze: Earned 100,000,000 credits (134,779,830)
Message 151409 - Posted: 6 Sep 2021 | 12:37:14 UTC

http://www.primegrid.com/stats_ww.php

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Profile BurProject donor
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Joined: 25 Feb 20
Posts: 514
ID: 1241833
Credit: 412,255,445
RAC: 18,902
321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,315,295)ESP LLR Ruby: Earned 2,000,000 credits (2,151,088)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,620,968)PPS LLR Jade: Earned 10,000,000 credits (15,382,679)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Ruby: Earned 2,000,000 credits (2,434,466)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Ruby: Earned 2,000,000 credits (2,027,649)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Turquoise: Earned 5,000,000 credits (5,096,952)AP 26/27 Turquoise: Earned 5,000,000 credits (5,797,662)GFN Jade: Earned 10,000,000 credits (10,874,159)WW Double Silver: Earned 200,000,000 credits (349,980,000)PSA Amethyst: Earned 1,000,000 credits (1,042,601)
Message 151411 - Posted: 6 Sep 2021 | 16:45:40 UTC - in response to Message 151409.

I meant a list of the smallest known |A| values. PG only lists the new results of this search, not already known ones.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

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Ravi Fernando
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Joined: 21 Mar 19
Posts: 210
ID: 1108183
Credit: 13,073,395
RAC: 6,263
321 LLR Amethyst: Earned 1,000,000 credits (1,061,204)Cullen LLR Silver: Earned 100,000 credits (111,878)ESP LLR Bronze: Earned 10,000 credits (16,570)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (68,801)PPS LLR Ruby: Earned 2,000,000 credits (4,610,019)PSP LLR Silver: Earned 100,000 credits (106,263)SoB LLR Silver: Earned 100,000 credits (258,849)SR5 LLR Bronze: Earned 10,000 credits (76,537)SGS LLR Silver: Earned 100,000 credits (148,878)TRP LLR Silver: Earned 100,000 credits (254,161)Woodall LLR Bronze: Earned 10,000 credits (97,444)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,001,667)AP 26/27 Bronze: Earned 10,000 credits (72,774)GFN Amethyst: Earned 1,000,000 credits (1,170,348)WW Bronze: Earned 10,000 credits (12,000)
Message 151412 - Posted: 6 Sep 2021 | 17:26:54 UTC
Last modified: 7 Sep 2021 | 16:22:05 UTC

Amazing find. It appears this is only the tenth twelfth known near-Wall-Sun-Sun prime with |A| = 1:

2 (+/-1)
3 (+1)
5 (+1)
17 (-1)
251 (-1)
733 (+1)
1063 (-1)
123863 (-1)
1677209 (+1)
6336823451747417 (-1)
104868559750360787 (+1)
7665762181374748069 (-1)

List from here. Signs from here--double-checked with WolframAlpha because that file has some known errors, including omitting 17. (Edit: tenth and eleventh from here; thanks JeppeSN.)

Also relevant (and now in need of an update) is JeppeSN's OEIS sequence A339855.

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Joined: 5 Apr 14
Posts: 1785
ID: 306875
Credit: 48,177,424
RAC: 13,351
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (593,283)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (112,799)PPS LLR Jade: Earned 10,000,000 credits (18,505,843)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (210,142)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (476,246)Woodall LLR Silver: Earned 100,000 credits (281,400)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (4,636,807)WW Jade: Earned 10,000,000 credits (13,756,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 151414 - Posted: 6 Sep 2021 | 21:16:11 UTC

O, why could it not be A=0 instead of A=-1? But still an amazing and improbable find! Congratulation, GregCinAZ.

I will update the OEIS sequence (first entry in Links, "Table of n, a(n) ...") mentioned by Ravi.

Note that PrimeGrid's near-Wall-Sun-Suns from the old PRPNet subproject can still be seen at https://u-g-f.de/PRPNet/findlist_adv.php?proj=WSS.

/JeppeSN

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Credit: 48,177,424
RAC: 13,351
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (593,283)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (112,799)PPS LLR Jade: Earned 10,000,000 credits (18,505,843)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (210,142)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (476,246)Woodall LLR Silver: Earned 100,000 credits (281,400)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (4,636,807)WW Jade: Earned 10,000,000 credits (13,756,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 151415 - Posted: 6 Sep 2021 | 21:56:51 UTC - in response to Message 151412.

Amazing find. It appears this is only the tenth known near-Wall-Sun-Sun prime with |A| = 1:

Twelfth, in fact (you miss 6336823451747417 and 104868559750360787). Will submit these twelve as A347565. /JeppeSN

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Ravi Fernando
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Joined: 21 Mar 19
Posts: 210
ID: 1108183
Credit: 13,073,395
RAC: 6,263
321 LLR Amethyst: Earned 1,000,000 credits (1,061,204)Cullen LLR Silver: Earned 100,000 credits (111,878)ESP LLR Bronze: Earned 10,000 credits (16,570)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (68,801)PPS LLR Ruby: Earned 2,000,000 credits (4,610,019)PSP LLR Silver: Earned 100,000 credits (106,263)SoB LLR Silver: Earned 100,000 credits (258,849)SR5 LLR Bronze: Earned 10,000 credits (76,537)SGS LLR Silver: Earned 100,000 credits (148,878)TRP LLR Silver: Earned 100,000 credits (254,161)Woodall LLR Bronze: Earned 10,000 credits (97,444)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,001,667)AP 26/27 Bronze: Earned 10,000 credits (72,774)GFN Amethyst: Earned 1,000,000 credits (1,170,348)WW Bronze: Earned 10,000 credits (12,000)
Message 151429 - Posted: 7 Sep 2021 | 16:27:03 UTC - in response to Message 151415.

Thanks, edited. If only all this information could be found in one place!

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Joined: 25 Feb 20
Posts: 514
ID: 1241833
Credit: 412,255,445
RAC: 18,902
321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,315,295)ESP LLR Ruby: Earned 2,000,000 credits (2,151,088)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,620,968)PPS LLR Jade: Earned 10,000,000 credits (15,382,679)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Ruby: Earned 2,000,000 credits (2,434,466)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Ruby: Earned 2,000,000 credits (2,027,649)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Turquoise: Earned 5,000,000 credits (5,096,952)AP 26/27 Turquoise: Earned 5,000,000 credits (5,797,662)GFN Jade: Earned 10,000,000 credits (10,874,159)WW Double Silver: Earned 200,000,000 credits (349,980,000)PSA Amethyst: Earned 1,000,000 credits (1,042,601)
Message 151438 - Posted: 8 Sep 2021 | 7:10:22 UTC
Last modified: 8 Sep 2021 | 7:12:32 UTC

Couldn't this sequence also be updated: A339855?

(there's another nice prime find pending validation since a few days, but I don't want to post it early...)
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

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Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 1785
ID: 306875
Credit: 48,177,424
RAC: 13,351
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (593,283)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (112,799)PPS LLR Jade: Earned 10,000,000 credits (18,505,843)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (210,142)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (476,246)Woodall LLR Silver: Earned 100,000 credits (281,400)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (4,636,807)WW Jade: Earned 10,000,000 credits (13,756,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 151440 - Posted: 8 Sep 2021 | 18:15:04 UTC - in response to Message 151438.

Couldn't this sequence also be updated: A339855?

It is updated. See first entry under LINKS. You may have to force your web browser to Update/Refresh/Reload after showing the plain text file because maybe it is confused by an old cache of b339855.txt. /JeppeSN

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Message boards : Wieferich and Wall-Sun-Sun Prime Search : WSS with A = -1 found!

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