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A059044
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Initial primes of sets of 5 consecutive primes in arithmetic progression. Each set has a constant difference of 30. These are the smallest of such primes.
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3
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9843019, 37772429, 53868649, 71427757, 78364549, 79080577, 98150021, 99591433, 104436889, 106457509, 111267419, 121174811, 121174841, 168236119, 199450099, 203908891, 207068803, 216618187, 230952859, 234058871, 235524781, 253412317
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OFFSET
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1,1
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COMMENTS
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It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. As of December 2000, the record is 10 primes.
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REFERENCES
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 181.
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..241 (all terms up to 3*10^9)
Index entries for sequences related to primes in arithmetic progressions
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FORMULA
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Found by exhaustive search for 5 primes in arithmetic progression with all other intermediate numbers being composite.
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MATHEMATICA
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Select[Partition[Prime[Range[14000000]], 5, 1], Length[Union[ Differences[ #]]]==1&] (* Harvey P. Dale, Jun 22 2013 *)
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CROSSREFS
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Cf. A033451 - 4 consecutive primes in arithmetic progression, A058362 - 6 consecutive primes in arithmetic progression
Sequence in context: A072867 A034606 A233839 * A107617 A234980 A179737
Adjacent sequences: A059041 A059042 A059043 * A059045 A059046 A059047
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KEYWORD
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nonn
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AUTHOR
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Harvey Dubner (harvey(AT)dubner.com), Dec 18 2000
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EXTENSIONS
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a(16)-a(22) from Donovan Johnson, Sep 05 2008
Reference added by Harvey P. Dale, Jun 22 2013
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STATUS
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approved
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