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A060770
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"Early" primes: upper ends of prime gaps that are smaller than the prime number theorem predicts.
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3
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3, 5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 47, 61, 71, 73, 83, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283, 311
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OFFSET
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1,1
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LINKS
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FORMULA
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A prime p belongs to the sequence iff p/log(p) - q/log(q) < 1 where q is the preceding prime.
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EXAMPLE
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11 is in the sequence because 11/log(11) - 7/log(7) = 0.990... < 1.
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PROG
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(PARI) { default(realprecision, 100); n=0; s=2/log(2); forprime (p=3, 12583, if ((r=p/log(p)) - s < 1, write("b060770.txt", n++, " ", p); ); s=r; ) } \\ Harry J. Smith, Jul 11 2009
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CROSSREFS
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Apart from 2 this is the complementary prime set to A060769.
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KEYWORD
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nonn
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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STATUS
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approved
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