A292618 The first prime of 8 consecutive primes a, b, c, d, e, f, g, h such that a + g = c + e and b + h = d + f.

359, 389, 839, 853, 937, 1019, 2213, 2221, 2237, 2593, 3019, 3821, 3823, 4111, 4231, 4801, 5407, 5839, 6997, 12241, 13499, 14741, 15473, 25603, 25771, 25793, 26393, 28597, 29297, 30839, 31147, 31543, 35051, 40487, 45281, 47933, 50023, 51827, 55061, 55441, 60343

Offset

1,1

Comments

In this condition, we can draw the following graphic whose sides are primes.

c

*------*

| |

d| |b

e | *---*

*------------* | a

| |

| |

| |

f| |h

| |

| g |

*---------------*

Dickson's conjecture implies that there are infinitely many prime octuplets of forms such as x, x+4, x+10, x+12, x+18, x+22, x+28, x+30, and thus infinitely many members of the sequence. - Robert Israel, Sep 20 2017

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Números y algo mas's blog, 1315 - Golígonos, Goliedros y demás.

Example

If a = 359, b, c, d, e, f, g, h = 367, 373, 379, 383, 389, 397, 401.

Maple

Primes:= select(isprime, [2, seq(i, i=3..10^5, 2)]):
Primes[select(i -> Primes[i]+Primes[i+6] = Primes[i+2]+Primes[i+4] and Primes[i+1]+Primes[i+7]=Primes[i+3]+Primes[i+5], [$1..nops(Primes)-7])];
# Robert Israel, Sep 20 2017

Prog

(PARI) forprime(p=1, 61000, my(v=primes([p, nextprime(nextprime(nextprime(nextprime(nextprime(nextprime(nextprime(p+1)+1)+1)+1)+1)+1)+1)])); if(v[1]+v[7]==v[3]+v[5] && v[2]+v[8]==v[4]+v[6], print1(p, ", "))) \\ Felix Fröhlich, Sep 20 2017

Crossrefs

Sequence in context: A280403 A145533 A273806 * A186461 A344285 A344286

Adjacent sequences: A292615 A292616 A292617 * A292619 A292620 A292621

Keyword

nonn

Author

Seiichi Manyama, Sep 20 2017

Status

approved