A222558 Least prime p such that 2*n*p is a sum of 10^6 subsequent primes.

3736971300983, 1868582442157, 1245659681423, 934275734321, 747425233469, 622762733249, 534156162737, 467093343419, 415824854441, 373728877943, 339743670103, 311538175027, 287741107327, 266994001331, 249114901193, 233613943273, 219815919913, 208214150917

Offset: 1

Author

Zak Seidov, Feb 25 2013

Keywords

• nonn

Comments

Indices of first primes are: 64, 89, 65, 81, 84, 13, 338, 35, 768, 105, 91, 256, 537, 186, 32, 174, 51, 1469, 519, 277, 2132, 232, 241, 310, 179, 744, 1835, 535, 787, 167, 664, 1538, 1253, 484, 620, 1450, 961, 649, 1472, 166, 480, 918, 107, 418, 173, 370, 871, 1967, 71, 534.

First primes are: 311, 461, 313, 419, 433, 41, 2273, 149, 5849, 571, 467, 1619, 3877, 1109, 131, 1033, 233, 12281, 3719, 1787, 18671, 1459, 1523, 2053, 1063, 5653, 15737, 3853, 6037, 991, 4967, 12917, 10211, 3461, 4583, 12109, 7573, 4817, 12323, 983, 3413, 7187, 587, 2887, 1031, 2531, 6763, 17047, 353, 3851.

Examples

			a(1) = 3736971300983 = (p(64)+...+p(1000063))/2 = (311 + ... + 15486871)/2.
a(2) = 1868582442157 = (p(89)+...+p(1000088))/4 = (461 + ... + 15487253)/4.
		

Crossrefs

Cf. A099824, A123086.

Programs

Mathematica

Do[s = 7472966967499 ; a = 2; b = 15485863; Do[s = s - a + (b = NextPrime[b]); a = NextPrime[a]; If[PrimeQ[s/m] , Print[{m, k, a, b, s/m}]; Break[]], {k, 2, 10^6}], {m, 2, 100, 2}]