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A126692
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Prime numbers p such that 1000-p is also a prime. All terms are shown.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Suggested by the Goldbach Conjecture.
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LINKS
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FORMULA
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p1 + p2 = 1000 where p1 and p2 are prime numbers.
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EXAMPLE
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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.
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MAPLE
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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
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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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PROG
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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
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CROSSREFS
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KEYWORD
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easy,fini,full,nonn
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AUTHOR
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STATUS
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approved
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