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
Examples
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.
Crossrefs
Cf. A126691.
Programs
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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
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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 *)
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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
Formula
p1 + p2 = 1000 where p1 and p2 are prime numbers.
Comments