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First in a sequence of 9 consecutive primes all of the form 4n+1.
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%I #8 Jun 21 2013 18:47:19

%S 11593,206953,315257,373649,373657,495377,495389,509389,509393,541097,

%T 612109,612113,766261,766273,766277,789097,789101,906541,992393,

%U 1124993,1330229,1330237,1410361,1531633,1531657,1531661,1578133,1578169,1595081,1694897,1694909

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

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

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

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

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

%K nonn

%O 1,1

%A _Harvey P. Dale_, Jun 21 2013