3 and 5 are twin primes, and the 3rd and 5th Fibonacci numbers are both prime. 5 and 7 are twin primes, and the 5th and 7th Fibonacci numbers are both prime. 11 and 13 are twin primes, and the 11th and 13th Fibonacci numbers are both prime. Are there any other twin prime pairs (p, p+2) such that the pth and (p+2)th Fibonacci numbers are both prime?

(In reply to Exploration by Charlie)

Using mathematica I was able to find the following solutions:
given as {p1,f(p1)} {p2,f(p2)}
1:
{3,2}
{5,5}
2:
{5,5}
{7,13}
3:
{11,89}
{13,233}
4: {431,529892711006095621792039556787784670197112759029534506620905162834769955134424689676262369} {433,1387277127804783827114186103186246392258450358171783690079918032136025225954602593712568353}
5: {569,36684474316080978061473613646275630451100586901195229815270242868417768061193560857904335017879540515228143777781065869} {571,96041200618922553823942883360924865026104917411877067816822264789029014378308478864192589084185254331637646183008074629}

Posted by Daniel on 2013-05-04 02:04:09