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A088483
Primes p such that p^2+p-1 and p^2+p+1 are twin primes.
13
2, 3, 5, 41, 59, 89, 101, 131, 743, 761, 1193, 2411, 2663, 2729, 3011, 3221, 3251, 3449, 4751, 6173, 6599, 6833, 7229, 8669, 9059, 9323, 9521, 9719, 9743, 10151, 10781, 11549, 11933, 12143, 12251, 12473, 12641, 13553, 13613, 14939, 15569, 16301
OFFSET
1,1
COMMENTS
Also primes in A155173 = Short leg A of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs... - Vladimir Joseph Stephan Orlovsky, Jan 21 2009
All terms >3 are congruent to 5 modulo 6. - Zak Seidov, Mar 21 2014
Intersection of A000040 and A088485. - Danny Rorabaugh, May 15 2017
EXAMPLE
a(7) = 101: 101*101 + 101 - 1 = 10301, 10301 and 10303 twin primes.
MATHEMATICA
lst={}; Do[p=Prime[n]; If[PrimeQ[p1=p*p+p-1]&&PrimeQ[p1+2], AppendTo[lst, p]], {n, 2*7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 21 2009 *)
Select[Prime[Range[2000]], AllTrue[#^2+#+{1, -1}, PrimeQ]&] (* Harvey P. Dale, Feb 22 2023 *)
PROG
(PARI) forprime(p=2, 1e5, if(isprime(p^2+p-1)&&isprime(p^2+p+1), print1(p", "))) \\ Charles R Greathouse IV, Dec 27 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Pierre CAMI, Nov 09 2003
STATUS
approved