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A178527
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Primes p such that either p - 2 or p + 2 has more than two distinct prime divisors.
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2
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103, 107, 163, 167, 193, 197, 229, 233, 257, 271, 283, 313, 317, 347, 359, 383, 397, 401, 431, 433, 457, 463, 467, 523, 557, 563, 587, 593, 607, 613, 617, 643, 647, 653, 661, 691, 733, 739, 743, 757, 761, 797, 821, 823, 827
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OFFSET
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1,1
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COMMENTS
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Sequence contains "many" pairs of cousin primes. More exactly, our conjectures are: (1) sequence contains almost all cousin primes; (2)for x >= 107, c(x)/A(x) > C(x)/pi(x), where A(x), c(x) and C(x) are the counting functions for this sequence, cousin pairs in this sequence and all cousin pairs respectively.
Indeed (a heuristic argument), a number n in the middle of a randomly chosen pair of cousin primes may be considered as a random integer.
The probability that n has no more than two prime divisors is, as well known, O((log(log n)/log n), i.e., it is natural to conjecture that almost all cousin pairs are in the sequence. Furthermore, it is natural to conjecture that the inequality is true as well, since A(x) < pi(x).
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LINKS
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MATHEMATICA
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Select[Prime[Range[200]], PrimeNu[# - 2] > 2 || PrimeNu[# + 2] > 2 &] (* Alonso del Arte, Dec 23 2010 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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