Extended Sierpinski Problem

In 1962, John Selfridge discovered the Sierpinski number k = 78557, which is believed to be the smallest such number. The Sierpinski problem attempts to prove that it is, in fact, the smallest Sierpinski number. In 1976, Nathan Mendelsohn determined that the second provable Sierpinski number is the prime k = 271129. The prime Sierpinski problem attempts to prove that this is the smallest prime Sierpinski number.

Should both of these problems be solved, k = 78557 will be established as the smallest Sierpinski number, and k = 271129 will be established as the smallest prime Sierpinski number. However, this would not prove that k = 271129 is the second provable Sierpinski number. Since the prime Sierpinski problem is testing all prime k's for 78557 < k < 271129, all that's needed is to test the composite k's for 78557 < k < 271129. Thus, the extended Sierpinski problem is established.

As of April 2018, there remains 10 composite k's for which no primes have been found. They are as follows:

91549, 99739, 131179, 163187, 200749, 202705, 209611, 227723, 229673, 238411

For a more detailed history and status of the extended Sierpinski problem, please visit Wilfrid Keller's The Sierpiński Problem: Definition and Status.

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Server Stats

Primes found by PrimeGrid
193997*2^11452891+1 found by Tom Greer on 3 April 2018

161041*2^7107964+1 found by Martin Vanc on 6 January 2015

211195*2^3224974+1 found by Ardo van Rangelrooij on 11 March 2013

94373*2^3206717+1 found by Jörg Meili on 10 March 2013

198677*2^2950515+1 found by Ardo van Rangelrooij on 23 October 2012

147559*2^2562218+1 found by Rodger Ewing on 27 March 2012

123287*2^2538167+1 found by Timothy D Winslow on 14 March 2012

250463*2^1316921+1 found by Rodger Ewing on 30 April 2010

219259*2^1300450+1 found by Lennart Vogel on 29 April 2010

154801*2^1305084+1 found by Rodger Ewing on 29 April 2010

98749*2^1045226+1 found by Rodger Ewing on 09 April 2010

107929*2^1007898+1 found by Brian Carpenter on 05 April 2010

85013*2^699333+1 found by Steve Martin on 25 March 2010

225679*2^620678+1 found by Lennart Vogel on 24 March 2010

187681*2^573816+1 found by Lennart Vogel on 23 March 2010

168587*2^545971+1 found by Steve Martin on 23 March 2010

208381*2^463068+1 found by Lennart Vogel on 22 March 2010

167957*2^417463+1 found by Brian Carpenter on 21 March 2010

185449*2^435402+1 found by Rodger Ewing on 21 March 2010

261203*2^354561+1 found by Lennart Vogel on 20 March 2010

227753*2^91397-1 found by Lennart Vogel 13 March 2010