

A195988


NearWieferich primes above 10^9: primes p>10^9 such that 2^((p1)/2) == +/1 + A*p (mod p^2) with A<=100, i.e., p=prime(i) such that A258367(i)<=100.


5



1222336487, 1259662487, 1274153897, 1494408397, 1584392531, 1586651309, 1662410923, 1817972423, 1890830857, 2062661389, 2244893621, 2332252547, 2416644757, 2461090421, 2566816313, 2570948153, 2589186937, 2709711233, 2760945133
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OFFSET

1,1


COMMENTS

There are many nearWieferich 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].
The choice of upper bound for A is rather arbitrary.


LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..139
R. Crandall, K. Dilcher and C. Pomerance, A search for Wieferich and Wilson primes, Math. Comp. Vol. 66, Num. 217 (1997), 433449.
J. Knauer and J. Richstein, The continuing search for Wieferich primes, Math. Comp. Vol. 74, Num. 251 (2005), 15591563.
R. McIntosh, EMail to Paul Zimmermann
PrimeGrid, Welcome to PrimeGrid PRPNet  Wieferich Prime Search  User Finds
PrimeGrid, Welcome to PrimeGrid's PRPNet Server (download prpclient package including wwww).
PrimeGrid, Wieferich & near Wieferich primes p < 11e15


PROG

(wwww) t Wieferich p 1e9 P 3e15 s 100


CROSSREFS

Cf. A001220, A246568, A258367, A258368.
Sequence in context: A166735 A104933 A119333 * A262996 A022250 A211770
Adjacent sequences: A195985 A195986 A195987 * A195989 A195990 A195991


KEYWORD

nonn


AUTHOR

Felix Fröhlich, Sep 26 2011


EXTENSIONS

Edited by Max Alekseyev, Dec 21 2011
New bfile from Felix Fröhlich, Aug 26 2015
Definition amended by Felix Fröhlich, Aug 29 2015


STATUS

approved



