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Twin prime indices of primes forming a twin prime member.
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%I #3 Oct 01 2013 17:57:43

%S 3,5,7,11,13,17,29,41,43,61,109,149,179,191,269,313,347,431,461,463,

%T 601,617,643,659,829,859,1031,1033,1051,1231,1279,1321,1619,1621,1879,

%U 1931,1949,1999,2029,2309,2311,2341,2383,2711,2789,2791,2801,3253,3299,3329

%N Twin prime indices of primes forming a twin prime member.

%C It is interesting that these primes occur rather frequently early on but gradually diminish as the iterations increase. Some ratios of count of twin primes p and the occurrence of prime(p) also a twin prime is as follows. Index< Ratio 1000 .74 10000 .48 100000 .39 1000000 .35 Looks like it is approaching a limit.

%e The 29th prime,109,is also a twin prime paired with the prime 107.

%o (PARI) twips(n) = { c1=0; c2=0; forprime(x=3,n, if(isprime(x+2),c1++); x1=prime(x); if(isprime(x-2) || isprime(x+2), if(isprime(x1-2) || isprime(x1+2), print1(x","); c2++; ) ) ); print(); print(c2/c1+.0) }

%K easy,nonn

%O 3,1

%A _Cino Hilliard_, Oct 21 2003