A086040 Prime p concatenated with next 4 primes is also prime.

7, 47, 53, 67, 97, 101, 149, 401, 431, 479, 487, 757, 827, 887, 1061, 1171, 1409, 1429, 1543, 1721, 1789, 1811, 1889, 1987, 2099, 2113, 2137, 2273, 2689, 2719, 2857, 3203, 3571, 3613, 3623, 3761, 3853, 3917, 3929, 4007, 4217, 4441, 4943, 5039, 5209, 5281, 5449

Offset: 1

Author

Chuck Seggelin, Jul 07 2003

Keywords

• base
• nonn

Examples

			a(1) = 7 because 7, 11, 13, 17 and 19 concatenated together yield 711131719, which is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030459, A030468, A030472, A086041.

Programs

Mathematica

Select[Partition[Prime[Range[800]],5,1],PrimeQ[FromDigits[Flatten[IntegerDigits/@#]]]&][[;;,1]] (* Harvey P. Dale, May 25 2025 *)

Python

from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    plst = [2, 3, 5, 7, 11]
    slst = list(map(str, plst))
    while True:
        if isprime(int("".join(slst))):
            yield plst[0]
        plst = plst[1:] + [nextprime(plst[-1])]
        slst = slst[1:] + [str(plst[-1])]
print(list(islice(agen(), 50))) # Michael S. Branicky, Jan 26 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, May 10 2012

a(15) and beyond from Michael S. Branicky, Jan 26 2023