**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

**attempts to prove that this is the smallest**

*prime*Sierpinski problem*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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### Primes found by PrimeGridEdit

**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