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A176619
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Primes p such that 2p + 3, 4p + 9, 3p + 2 and 9p + 8 are also primes.
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0
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5, 7, 97, 167, 397, 607, 2617, 2707, 7687, 12097, 14407, 16787, 19577, 22307, 23827, 24967, 25717, 28547, 31687, 43037, 43517, 46817, 58967, 59617, 63607, 70237, 70957, 78517, 85027, 96797
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OFFSET
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1,1
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COMMENTS
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These primes stay prime under two iterations of p->2p+3 as well as under two iterations of p->3p+2.
For all entries >5 the least significant digit is 7.
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REFERENCES
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Joe Buhler: Algorithmic Number Theory: Third International Symposium, ANTS-III, Springer New York, 1998
F. Ischebeck: Einladung zur Zahlentheorie, B. I. Wissenschaftsverlag, Mannheim-Leipzig-Wien-Zuerich, 1992
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LINKS
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FORMULA
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EXAMPLE
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2*5 + 3 = 13 = prime(6),
4*5 + 9 = 29 = prime(10),
3*5 + 2 = 17 = prime(7),
9*5 + 8 = 53 = prime(16); 5 = prime(3) = a(1).
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PROG
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(Magma) [p: p in PrimesUpTo(100000)|IsPrime(2*p+3) and IsPrime(4*p+9) and IsPrime(3*p+2) and IsPrime(9*p+8 )] // Vincenzo Librandi, Jan 29 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 22 2010
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STATUS
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approved
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