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A136287
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Numbers k such that k*(k+1) - 1 and k*(k+3) - 1 are both the initial member of a pair of twin primes and Sophie Germain primes. In other words, k*(k+1) - 1, k*(k+1) + 1, k*(k+3) - 1, k*(k+3) + 1, 2*k*(k+1) - 1, 2*k*(k+3) - 1 are all primes.
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0
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3727470, 16547895, 20983605, 25649085, 27563745, 27906165, 38221260, 41232960, 55136850, 70584030, 72097305, 78362415, 91531320, 94746750, 121155165, 134647800, 134660370, 141473715, 150940515, 188741475, 261431820, 275356290, 275952675, 276220965, 307341165, 311631255
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OFFSET
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1,1
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COMMENTS
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For k = 134467800, 275356290 and 443034450, 2*k*(k+1) + 1 is also prime.
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LINKS
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PROG
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(PARI) is(k) = !(k%15) && isprime(k*(k+1)-1) && isprime(k*(k+1)+1) && isprime(k*(k+3)-1) && isprime(k*(k+3)+1) && isprime(2*k*(k+1)-1) && isprime(2*k*(k+3)-1); \\ Jinyuan Wang, Mar 20 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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