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A195988 Near-Wieferich primes above 10^9: primes p > 10^9 such that 2^((p-1)/2) == +-1 + A*p (mod p^2) with |A| <= 100, i.e., p=prime(i) such that A258367(i) <= 100.

%I A195988 #48 Apr 28 2022 07:47:08
%S A195988 1222336487,1259662487,1274153897,1494408397,1584392531,1586651309,
%T A195988 1662410923,1817972423,1890830857,2062661389,2244893621,2332252547,
%U A195988 2416644757,2461090421,2566816313,2570948153,2589186937,2709711233,2760945133
%N A195988 Near-Wieferich primes above 10^9: primes p > 10^9 such that 2^((p-1)/2) == +-1 + A*p (mod p^2) with |A| <= 100, i.e., p=prime(i) such that A258367(i) <= 100.
%C A195988 There are many near-Wieferich primes below 10^9 (including Wieferich primes 1093 and 3511). However, Crandall, Dilcher and Pomerance searched and reported such primes in the interval [10^9, 4*10^12].
%C A195988 The choice of upper bound for |A| is rather arbitrary.
%H A195988 Jeppe Stig Nielsen, <a href="/A195988/b195988.txt">Table of n, a(n) for n = 1..149</a> (terms n = 1..139 from Felix Fröhlich)
%H A195988 R. Crandall, K. Dilcher and C. Pomerance, <a href="https://doi.org/10.1090/S0025-5718-97-00791-6">A search for Wieferich and Wilson primes</a>, Math. Comp. Vol. 66, Num. 217 (1997), 433-449.
%H A195988 J. Knauer and J. Richstein, <a href="https://doi.org/10.1090/S0025-5718-05-01723-0">The continuing search for Wieferich primes</a>, Math. Comp. Vol. 74, Num. 251 (2005), 1559-1563.
%H A195988 R. McIntosh, <a href="http://www.loria.fr/~zimmerma/records/Wieferich.status">E-Mail to Paul Zimmermann</a>
%H A195988 PrimeGrid, <a href="https://web.archive.org/web/20201126000718/https://www.primegrid.com/download/wieferich_list.pdf">Wieferich & near Wieferich Primes p < 11e15</a>
%H A195988 PrimeGrid, <a href="https://www.primegrid.com/stats_ww.php">WW Statistics</a>
%Y A195988 Cf. A001220, A246568, A258367, A258368.
%K A195988 nonn
%O A195988 1,1
%A A195988 _Felix Fröhlich_, Sep 26 2011
%E A195988 Edited by _Max Alekseyev_, Dec 21 2011
%E A195988 New b-file from _Felix Fröhlich_, Aug 26 2015
%E A195988 Definition amended by _Felix Fröhlich_, Aug 29 2015