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Lower twin primes p such that 6*p-1 and 6*p+1 are twin primes and (p+1)/6 is prime.
1

%I #16 Jan 29 2023 17:30:38

%S 17,137,23537,92957,157217,318677,326657,440177,510617,521537,558497,

%T 577937,617717,651017,661097,861437,969257,1093997,1152077,1168337,

%U 1177157,1260317,1299917,1356077,1463177,1514657,1600097,1617437,1768757,1773977,1957937,2065577,2271497,2335637,2382557,2450597

%N Lower twin primes p such that 6*p-1 and 6*p+1 are twin primes and (p+1)/6 is prime.

%H Robert Israel, <a href="/A358202/b358202.txt">Table of n, a(n) for n = 1..1000</a>

%e a(2) = 137 is a term because 137 and 139 are twin primes, 6*137-1 = 821 and 6*137+1 = 823 are twin primes, and (137+1)/6 = 23 is a prime.

%p P:= select(isprime, {seq(i,i=5..2*10^7,2)}):

%p T:= P intersect map(`-`,P,2):

%p R:=T intersect map(t -> (t+1)/6, T):

%p sort(convert(select(t -> isprime((t+1)/6), R),list));

%t Select[Prime[Range[180000]], PrimeQ[# + 2] && PrimeQ[6*# - 1] && PrimeQ[6*# + 1] && PrimeQ[(# + 1)/6] &] (* _Amiram Eldar_, Nov 03 2022 *)

%t Select[Prime[Range[180000]],AllTrue[{#+2,6#+1,6#-1,(#+1)/6},PrimeQ]&] (* _Harvey P. Dale_, Jan 29 2023 *)

%Y Intersection of A060213 and A176131.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Nov 03 2022