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A059044 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. 3
9843019, 37772429, 53868649, 71427757, 78364549, 79080577, 98150021, 99591433, 104436889, 106457509, 111267419, 121174811, 121174841, 168236119, 199450099, 203908891, 207068803, 216618187, 230952859, 234058871, 235524781, 253412317 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. As of December 2000, the record is 10 primes.

REFERENCES

David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 181.

LINKS

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

FORMULA

Found by exhaustive search for 5 primes in arithmetic progression with all other intermediate numbers being composite.

MATHEMATICA

Select[Partition[Prime[Range[14000000]], 5, 1], Length[Union[ Differences[ #]]]==1&] (* Harvey P. Dale, Jun 22 2013 *)

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Harvey Dubner (harvey(AT)dubner.com), Dec 18 2000

EXTENSIONS

a(16)-a(22) from Donovan Johnson, Sep 05 2008

Reference added by Harvey P. Dale, Jun 22 2013

STATUS

approved

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Last modified August 18 03:18 EDT 2017. Contains 290682 sequences.