A261701 Initial member of four twin prime pairs with gap 210 between them.
599, 3917, 5021, 37361, 48779, 81929, 93281, 97157, 263399, 433049, 783149, 821801, 906119, 908669, 1197197, 1308497, 1308707, 1379237, 1464809, 1908449, 2036861, 2341979, 2408561, 2760671, 2804309, 3042491, 3042701, 3042911, 3198197, 4090649, 4543991, 5543927
Offset: 1
Keywords
Examples
599 appears in the sequence because: (a) {599,601}, {809, 811}, {1019, 1021}, {1229, 1231} are four (not consecutive) twin prime pairs; (b) the gap between each twin prime pair (809 - 599) = (1019 - 809) = (1229 - 1019) = 210.
Links
- K. D. Bajpai and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 865 terms from K. D. Bajpai]
- Luis Rodriguez and Carlos Rivera, Gaps between consecutive twin pairs, The Prime Puzzles and Problems Connection.
Programs
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Magma
[p: p in PrimesUpTo (100000) | IsPrime(p+2) and IsPrime(p+210) and IsPrime(p+212) and IsPrime(p+420) and IsPrime(p+422) and IsPrime(p+630) and IsPrime(p+632) ];
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Maple
select(p -> andmap(isprime, [p, p+2, p+210, p+212, p+420, p+422, p+630, p+632]),[seq(p, p=1..10^5)]);
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Mathematica
k = 210; Select[Prime@Range[10^7], PrimeQ[# + 2] && PrimeQ[# + k] && PrimeQ[# + k + 2] && PrimeQ[# + 2 k] && PrimeQ[# + 2 k + 2] && PrimeQ[# + 3 k] && PrimeQ[# + 3 k + 2] &] Select[Prime[Range[400000]],AllTrue[#+{2,210,212,420,422,630,632},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 17 2019 *) -
PARI
forprime(p= 1, 100000, if(isprime(p+2) && isprime(p+210) && isprime(p+212) && isprime(p+420) && isprime(p+422) && isprime(p+630) && isprime(p+632), print1(p,", ")));
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Perl
use ntheory ":all"; say join ", ", grep { is_prime($+210) && is_prime($+212) && is_prime($+420) && is_prime($+422) && is_prime($+630) && is_prime($+632) } @{twin_primes(1e8)}; # Dana Jacobsen, Sep 02 2015 -
Perl
use ntheory ":all"; say for sieve_prime_cluster(1, 1e8, 2, 210, 212, 420, 422, 630, 632); # Dana Jacobsen, Oct 03 2015
Comments