A126692 Prime numbers p such that 1000-p is also a prime. All terms are shown.

3, 17, 23, 29, 47, 53, 59, 71, 89, 113, 137, 173, 179, 191, 227, 239, 257, 281, 317, 347, 353, 359, 383, 401, 431, 443, 479, 491, 509, 521, 557, 569, 599, 617, 641, 647, 653, 683, 719, 743, 761, 773, 809, 821, 827, 863, 887, 911, 929, 941, 947, 953, 971, 977, 983, 997

Offset

1,1

Comments

Suggested by the Goldbach Conjecture.

Links

Table of n, a(n) for n=1..56.

Formula

p1 + p2 = 1000 where p1 and p2 are prime numbers.

Example

3 + 997 = 17 + 983 = 23 + 977 = 29 + 971 = 47 + 953 = 53 + 947 = 59 + 941 = 71 + 929 = 89 + 911 = 113 + 887 = 137 + 863 = 173 + 827 = 179 + 821 = 191 + 809 = 227 + 773 = 239 + 761 = 257 + 743 = 281 + 719 = 317 + 683 = 347 + 653 = 353 + 647 = 359 + 641 = 383 + 617 = 401 + 599 = 431 + 569 = 443 + 557 = 479 + 521 = 491 + 509 = 1000.

Maple

a:= proc(n) if isprime(n) and isprime(1000-n) then n fi end: seq(a(n), n=1..1000); # Emeric Deutsch, Feb 16 2007

Mathematica

Select[Prime[Range[PrimePi[1000]]], PrimeQ[1000-#]&] (* Harvey P. Dale, Nov 28 2011 *)
Flatten[Select[IntegerPartitions[1000, {2}], AllTrue[#, PrimeQ]&]]//Sort (* Harvey P. Dale, Jul 30 2023 *)

Prog

(Python)
from sympy import isprime, primerange
print(sorted(p for p in primerange(1, 1000) if isprime(1000-p))) # Michael S. Branicky, Mar 17 2021

Crossrefs

Cf. A126691.

Sequence in context: A019369 A019380 A296937 * A057173 A109371 A272176

Adjacent sequences: A126689 A126690 A126691 * A126693 A126694 A126695

Keyword

easy,fini,full,nonn

Author

Tomas Xordan, Feb 14 2007

Status

approved