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 A180247 Prime Brier numbers: primes p such that for all k >= 1 the numbers p*2^k + 1 and p*2^k - 1 are composite. 16
 10439679896374780276373, 21444598169181578466233, 105404490005793363299729, 178328409866851219182953, 239365215362656954573813, 378418904967987321998467, 422280395899865397194393, 474362792344501650476113, 490393518369132405769309 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS WARNING: These are just the smallest examples known - there may be smaller ones. Even the first term is uncertain. - N. J. A. Sloane, Jun 20 2017 There are no prime Brier numbers below 10^10. - Arkadiusz Wesolowski, Jan 12 2011 It is a conjecture that every such number has more than 11 digits. In 2011 I have calculated that for any prime p < 10^11 there is a k such that either p*2^k + 1 or p*2^k - 1 has all its prime factors greater than 1321. - Arkadiusz Wesolowski, Feb 03 2016 The first term was found by Dan Ismailescu and Peter Seho Park and the next two by Christophe Clavier (see below). See also A076335. - N. J. A. Sloane, Jan 03 2014 a(4)-a(9) computed in 2017 by the author. LINKS D. Baczkowski, J. Eitner, C. E. Finch, B. Suminski, and M. Kozek, Polygonal, Sierpinski, and Riesel numbers, Journal of Integer Sequences, 2015 Vol 18. #15.8.1. Chris Caldwell, The Prime Glossary, Riesel number Chris Caldwell, The Prime Glossary, Sierpinski number Christophe Clavier, 14 new Brier numbers Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), pp. 79-81. P. Erdős, On integers of the form 2^k + p and some related problems, Summa Brasil. Math. 2 (1950), pp. 113-123. Yves Gallot, A search for some small Brier numbers, 2000. G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6992565235279559197457863 Dan Ismailescu and Peter Seho Park, On Pairwise Intersections of the Fibonacci, Sierpiński, and Riesel Sequences, Journal of Integer Sequences, 16 (2013), #13.9.8. Joe McLean, Brier Numbers [Cached copy] Carlos Rivera, Problem 52. ±p ± 2^n, The Prime Puzzles and Problems Connection. Eric Weisstein's World of Mathematics, Brier Number CROSSREFS Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639, A076336, A076337, A040081, A040076, A103963, A103964, A038699, A050921, A064699, A052333, A003261. These are the primes in A076335. Sequence in context: A115542 A330009 A171265 * A095440 A326414 A162033 Adjacent sequences:  A180244 A180245 A180246 * A180248 A180249 A180250 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Aug 19 2010 EXTENSIONS Entry revised by N. J. A. Sloane, Jan 03 2014 Entry revised by Arkadiusz Wesolowski, May 29 2017 STATUS approved

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Last modified May 13 14:47 EDT 2021. Contains 343860 sequences. (Running on oeis4.)