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Message boards : The Riesel Problem : It is conjectured that k=509203 is the smallest Riesel number. Or what?

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Michael Millerick
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Joined: 4 Feb 09
Posts: 743
ID: 35074
Credit: 199,599,590
RAC: 0
Found 3 primes in the 2020 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,063,954)Cullen LLR Amethyst: Earned 1,000,000 credits (1,328,304)ESP LLR Turquoise: Earned 5,000,000 credits (8,170,793)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,319,313)PPS LLR Jade: Earned 10,000,000 credits (14,623,895)PSP LLR Ruby: Earned 2,000,000 credits (2,012,651)SoB LLR Amethyst: Earned 1,000,000 credits (1,064,898)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Amethyst: Earned 1,000,000 credits (1,320,684)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Amethyst: Earned 1,000,000 credits (1,492,539)321 Sieve Turquoise: Earned 5,000,000 credits (5,440,175)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,911,344)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,077,092)PPS Sieve Emerald: Earned 50,000,000 credits (50,200,870)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,034,014)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,774)AP 26/27 Turquoise: Earned 5,000,000 credits (5,442,696)GFN Sapphire: Earned 20,000,000 credits (33,288,606)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 53555 - Posted: 30 Apr 2012 | 0:52:09 UTC - in response to Message 53553.

The conjecture is:
k=509203 is the smallest number such that k*2^n-1 is composite for all natural n.

191249*2^3417696-1 being prime proves that k=191249 does not meet the criterion for the conjecture (since that means there exists an n such that 191249*2^n-1 is prime).
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Profile DaveBProject donor
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Joined: 20 Jun 09
Posts: 351
ID: 42198
Credit: 11,898,570
RAC: 0
321 LLR Gold: Earned 500,000 credits (547,769)Cullen LLR Silver: Earned 100,000 credits (158,867)PPS LLR Silver: Earned 100,000 credits (162,534)PSP LLR Silver: Earned 100,000 credits (134,373)SoB LLR Gold: Earned 500,000 credits (510,012)SR5 LLR Silver: Earned 100,000 credits (266,757)SGS LLR Gold: Earned 500,000 credits (510,560)TRP LLR Silver: Earned 100,000 credits (242,439)Woodall LLR Gold: Earned 500,000 credits (508,989)321 Sieve Silver: Earned 100,000 credits (200,123)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (229,801)PPS Sieve Ruby: Earned 2,000,000 credits (4,317,221)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (21,147)TRP Sieve (suspended) Silver: Earned 100,000 credits (333,494)AP 26/27 Bronze: Earned 10,000 credits (24,117)GFN Ruby: Earned 2,000,000 credits (3,730,320)
Message 53559 - Posted: 30 Apr 2012 | 9:19:00 UTC

Unfortunatly this means that if 509203 is not the smallest Riesel number then we cannot ever prove a smaller one, as the test of any riesel number by PG will go on to infinity!
____________
Member team AUSTRALIA
My lucky number is 9291*2^1085585+1

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TroubledBunnyProject donor
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Joined: 4 Jun 07
Posts: 607
ID: 8931
Credit: 470,669,737
RAC: 0
Discovered 1 mega prime321 LLR Amethyst: Earned 1,000,000 credits (1,004,625)Cullen LLR Amethyst: Earned 1,000,000 credits (1,019,085)ESP LLR Amethyst: Earned 1,000,000 credits (1,006,207)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,148,385)PPS LLR Ruby: Earned 2,000,000 credits (4,011,256)PSP LLR Ruby: Earned 2,000,000 credits (2,115,686)SoB LLR Ruby: Earned 2,000,000 credits (2,357,348)SR5 LLR Ruby: Earned 2,000,000 credits (2,050,964)SGS LLR Amethyst: Earned 1,000,000 credits (1,175,581)TRP LLR Amethyst: Earned 1,000,000 credits (1,109,064)Woodall LLR Amethyst: Earned 1,000,000 credits (1,606,752)321 Sieve Ruby: Earned 2,000,000 credits (2,113,919)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,655,968)Generalized Cullen/Woodall Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,006,509)PPS Sieve Double Silver: Earned 200,000,000 credits (347,222,280)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,014,690)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,141,121)AP 26/27 Ruby: Earned 2,000,000 credits (2,764,542)GFN Emerald: Earned 50,000,000 credits (76,867,118)PSA Jade: Earned 10,000,000 credits (16,276,495)
Message 53563 - Posted: 30 Apr 2012 | 10:20:14 UTC - in response to Message 53559.

Unfortunatly this means that if 509203 is not the smallest Riesel number then we cannot ever prove a smaller one, as the test of any riesel number by PG will go on to infinity!

So, just to reiterate..

It is exactly the opposite of DaveB's comment that we are hoping for:
509203 is the smallest Riesel number and we will prove it (by finding primes for the remaining Ks) within a finite time.

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Message boards : The Riesel Problem : It is conjectured that k=509203 is the smallest Riesel number. Or what?

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