A237890 Primes p such that p^2 + 4 and p^2 + 10 are also primes.
3, 7, 13, 97, 487, 613, 743, 827, 883, 1117, 1987, 2477, 2887, 3863, 4483, 5153, 5557, 5683, 5923, 5953, 6287, 7643, 7937, 8093, 9323, 10343, 12377, 13033, 13063, 14087, 14767, 15373, 16937, 17713, 17987, 18257, 19013, 19333, 19753, 19853, 20287, 20873, 21673
Offset: 1
Keywords
Examples
7 is prime and appears in the sequence because 7^2+4 = 53 and 7^2+10 = 59 are also primes. 97 is prime and appears in the sequence because 97^2+4 = 9413 and 97^2+10 = 9419 are also primes.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..1300
Programs
-
Maple
KD := proc() local a,b,d; a:=ithprime(n); b:=a^2+4; d:=a^2+10; if isprime (b) and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..5000);
-
Mathematica
Select[Prime[Range[5000]], PrimeQ[#^2 + 4] && PrimeQ[#^2 + 10] &]
-
PARI
s=[]; forprime(p=2, 25000, if(isprime(p^2+4) && isprime(p^2+10), s=concat(s, p))); s \\ Colin Barker, Feb 15 2014