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.

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

Offset: 1

Author

Felix Fröhlich, Sep 26 2011

Keywords

• nonn

Comments

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].

The choice of upper bound for |A| is rather arbitrary.

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..149 (terms n = 1..139 from Felix Fröhlich)
• R. Crandall, K. Dilcher and C. Pomerance, A search for Wieferich and Wilson primes, Math. Comp. Vol. 66, Num. 217 (1997), 433-449.
• J. Knauer and J. Richstein, The continuing search for Wieferich primes, Math. Comp. Vol. 74, Num. 251 (2005), 1559-1563.
• R. McIntosh, E-Mail to Paul Zimmermann
• PrimeGrid, Wieferich & near Wieferich Primes p < 11e15
• PrimeGrid, WW Statistics

Crossrefs

Cf. A001220, A246568, A258367, A258368.

Extensions

Edited by Max Alekseyev, Dec 21 2011

New b-file from Felix Fröhlich, Aug 26 2015

Definition amended by Felix Fröhlich, Aug 29 2015