A226905 First in a sequence of 9 consecutive primes all of the form 4n+1.

11593, 206953, 315257, 373649, 373657, 495377, 495389, 509389, 509393, 541097, 612109, 612113, 766261, 766273, 766277, 789097, 789101, 906541, 992393, 1124993, 1330229, 1330237, 1410361, 1531633, 1531657, 1531661, 1578133, 1578169, 1595081, 1694897, 1694909

Offset: 1

Author

Harvey P. Dale, Jun 21 2013

Keywords

• nonn

Examples

			206953, 206993, 207013, 207017, 207029, 207037, 207041, 207061, and 207073 are 9 consecutive primes, each equal to 1 mod 4.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 163 (entry for 11593).

Crossrefs

Cf. A055623 (first occurrence of run of primes congruent to 1 mod 4 of exactly length n).

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[180000]],9,1],Union[Mod[#,4]] == {1}&]][[1]]