A167417 Largest prime concatenation of the first n primes, or 0 if no such prime exists.

2, 23, 523, 7523, 751123, 75311213, 7523171311, 753217131911, 75323219131117, 0, 753312923219111713, 75373312923192171311, 7541373132923217111319, 754341373132923192171311, 75474341373132923211171319

Offset

1,1

Comments

a(10) doesn't exist, because the sum of digits of the first 10 primes (2+3+5+7+(1+1)+(1+3)+(1+7)+(1+9)+(2+3)+(2+9)) = 57 is a multiple of 3.

References

Richard E. Crandall and Carl Pomerance, Prime Numbers, Springer 2005.

Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996.

A. Weil, Number theory: an approach through history, Birkhäuser 1984.

Links

Table of n, a(n) for n=1..15.

Gleb Ivanov, Python program for large terms.

Example

The only prime concatenations of the first n primes for n = 1..3 are a(1)=2, a(2)=23, and a(3)=523.
For n=4, the only prime concatenations of 2, 3, 5, and 7 are 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523; the largest of these is a(4) = 7523.

Prog

(Python)
from sympy import sieve, isprime
from itertools import permutations
for n in range(1, 14):
    sieve.extend_to_no(n)
    p = list(map(str, list(sieve._list)))[:n]
    mint = 0
    for i in permutations(p, len(p)):
        t = int(''.join(i))
        if  t > mint and isprime(t):
            mint = t
    print(mint, end = ', ') # Gleb Ivanov, Dec 05 2021

Crossrefs

Cf. A175429, A177275, A134966, A167416.

Sequence in context: A053160 A167416 A053066 * A053161 A090731 A379867

Adjacent sequences: A167414 A167415 A167416 * A167418 A167419 A167420

Keyword

nonn,base

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 03 2009

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010

Several terms corrected and a(11)-a(15) from Gleb Ivanov, Dec 05 2021

Status

approved