A126693 Prime numbers p such that 10000-p is also a prime.

59, 71, 113, 149, 167, 197, 233, 251, 257, 281, 311, 449, 461, 467, 479, 503, 509, 521, 563, 569, 587, 659, 677, 719, 743, 761, 773, 797, 827, 839, 863, 941, 971, 1031, 1049, 1151, 1163, 1181, 1193, 1217, 1259, 1301, 1307, 1319, 1373, 1427, 1487, 1499, 1553

Offset: 1

Author

Tomas Xordan, Feb 14 2007

Keywords

• easy
• fini
• full
• nonn

Comments

Suggested by the Goldbach conjecture. The last term of this sequence is a(254)=9941.

Examples

			(59 + 9941) = (71 + 9929) = (113 + 9887) = (149 + 9851) = (167 + 9833) = (197 + 9803) = (233 + 9767) = (251 + 9749) = (257 + 9743) = (281 + 9719) = (311 + 9689) = ... = 10000.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..254 (full sequence)

Programs

Maple

a:=proc(n) if isprime(n) and isprime(10000-n) then n fi end: seq(a(n), n=1..10000); # Emeric Deutsch, Feb 16 2007

Mathematica

Select[Prime[Range[PrimePi[10000]]],PrimeQ[10000-#]&] (* Harvey P. Dale, Mar 04 2013 *)

Formula

p1+p2 = 10000 where p1 and p2 are prime numbers.