A243916 Largest safe prime less than 2^n.

7, 11, 23, 59, 107, 227, 503, 1019, 2039, 4079, 8147, 16223, 32603, 65267, 130787, 262127, 524243, 1048343, 2097143, 4194287, 8388287, 16776899, 33553799, 67108187, 134217323, 268435019, 536870723, 1073740439, 2147483579, 4294967087

Offset

3,1

Comments

Largest safe prime (A005385) p=2*q+1, q also prime (A005384), that can be represented using n binary digits.

Links

Gokberk Yaltirakli, Table of n, a(n) for n = 3..1024 (terms 3..100 from Harvey P. Dale)

Mathematica

lsp[n_]:=Module[{sp=NextPrime[2^n, -1]}, While[!PrimeQ[(sp-1)/2], sp= NextPrime[ sp, -1]]; sp]; Array[lsp, 35, 3] (* Harvey P. Dale, Feb 10 2019 *)

Prog

(Scheme) ;; With Aubrey Jaffer's SLIB Scheme library
(require 'factor) ;; For prime? predicate.
(define (A243916 n) (if (< n 3) 0 (let loop ((i (- (expt 2 n) 1))) (cond ((and (prime? i) (prime? (/ (- i 1) 2))) i) (else (loop (- i 2)))))))
;; Antti Karttunen, Jun 18 2014
(Python)
from sympy import isprime
def a(n):
    if n<3: return 0
    i=2**n - 1
    while True:
        if isprime(i) and isprime((i - 1)/2): return i
        else: i-=2 # Indranil Ghosh, Jun 12 2017, after Antti Karttunen's Scheme Code

Crossrefs

Cf. A005385, A005384, A000079.

Sequence in context: A140111 A118072 A141305 * A181841 A076855 A160054

Adjacent sequences: A243913 A243914 A243915 * A243917 A243918 A243919

Keyword

nonn

Author

José Eduardo Gaboardi de Carvalho, Jun 18 2014

Status

approved