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A217577
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The only prime p such that k*a < p < k*b where a, b are consecutive primes, case k=5.
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6
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89, 211, 359, 509, 541, 691, 751, 991, 1201, 1399, 1409, 1559, 1741, 2099, 2161, 2179, 2333, 2503, 2609, 2851, 3089, 3209, 3271, 4111, 4139, 4289, 4297, 4409, 5309, 5591, 6151, 6389, 6397, 6491, 6599, 7283, 7411, 7993, 8039, 8101, 8467, 8609, 8941, 9391, 9661
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OFFSET
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1,1
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COMMENTS
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Corresponding values of b-a: 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 4, 4, 2, 2, 2, 2, 6, 2, 2, 2, 4, 2, 2, 6, 2, 2, 4, 4, 2, 6. In most cases b-a = 2. Smallest n for which b-a = 2(2)26: 1, 10, 16, 62, 119, 414, 939, 2565, 1349, 1042, 10470, 22211, 23553. Also, at n = 43461, b-a = 32.
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LINKS
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EXAMPLE
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89 is the only prime in the interval [5*17, 5*19] = [85,95],
211 is the only prime in the interval [5*41, 5*43] = [205,215],
359 is the only prime in the interval [5*71, 5*73] = [355,365].
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MATHEMATICA
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a = 2; b = 3; s = {}; k = 5; Do[If[(p = NextPrime[k*a]) < k*b && NextPrime[p] > k*b, AppendTo[s, p]]; a = b; b = NextPrime[b], {100}]; s
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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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