A189571 Smallest of nine consecutive primes whose sum is a prime.

3, 29, 31, 37, 47, 79, 83, 89, 107, 109, 127, 131, 139, 149, 157, 173, 179, 193, 197, 199, 211, 241, 277, 347, 359, 367, 373, 389, 397, 433, 449, 487, 491, 521, 577, 593, 619, 643, 659, 677, 743, 761, 829, 853, 953, 977, 1049, 1063, 1087, 1129, 1151, 1193

Offset: 1

Author

Bruno Berselli, Apr 23 2011

Keywords

• nonn

Comments

First 7-tuple of consecutive primes belonging to the sequence: 118061, 118081, 118093, 118127, 118147, 118163, 118169. Twin primes in the sequence: 29, 31; 107, 109; 197, 199; 1427, 1429; 1607, 1609; 1721, 1723; 4019, 4021, etc. [Bruno Berselli, Aug 26 2013]

Examples

			47 is in the sequence because 47+53+59+61+67+71+73+79+83 = 593 and 593 is prime.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073681, A152468, A180948, A180950, A226380.

Programs

Magma

[ NthPrime(n): n in [1..190] | IsPrime(&+[NthPrime(n+s): s in [0..8]]) ];

Mathematica

Transpose[Select[Partition[Prime[Range[500]],9,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)

Python

from sympy import isprime, nextprime
def aupto(limit):
  plst, alst = [3, 5, 7, 11, 13, 17, 19, 23, 29], []
  while plst[0] <= limit:
    if isprime(sum(plst)): alst.append(plst[0])
    plst = plst[1:] + [nextprime(plst[-1])]
  return alst
print(aupto(1200)) # Michael S. Branicky, Mar 29 2021

Extensions

Additional cross reference from Harvey P. Dale, Jun 05 2013