A327915 The 59 prime dates of each leap year of the form concatenate(month,day) with leading zero for days 1..9.

101, 103, 107, 109, 113, 127, 131, 211, 223, 227, 229, 307, 311, 313, 317, 331, 401, 409, 419, 421, 503, 509, 521, 523, 601, 607, 613, 617, 619, 701, 709, 719, 727, 809, 811, 821, 823, 827, 829, 901, 911, 919, 929, 1009, 1013, 1019, 1021, 1031, 1103, 1109, 1117, 1123, 1129, 1201, 1213, 1217, 1223, 1229, 1231

Offset: 1

Author

Wolfdieter Lang, Sep 30 2019

Keywords

• nonn
• easy
• fini
• full

Comments

In leap years all these dates come from the months January, February, ..., December, in the form m.d, with a 0 in front of the days d = 1..9, with 7, 4, 5, 4, 4, 5, 4, 6, 4, 5, 5, 6 prime dates, respectively, adding up to 59. For the corresponding leap year case with 58 prime dates see A327914.

Compared with A327349 (leap years, no 0's before days d = 1..9) one has the same differences as given in a comment in A327914 (229 appears in the present sequence and in A327349).

Crossrefs

Cf. A327346 (74 prime dates d.m without leading 0 for month), A327347 (54 prime dates d.m with leading 0 for months m = 1, 3, 7, 9), A327348 (66 prime dates m.d for non-leap years), A327349 (67 prime dates, like A327348 but for leap years), A327914 (58 prime dates, the case for non-leap years).

Programs

Mathematica

Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[m~Join~PadLeft[IntegerDigits[#], 2]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 29, True, 31]} &, 12], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)
fd[{m_,d_}]:=FromDigits[Flatten[{m,PadLeft[{d},2,0]}]]; Select[fd[Take[#,{2,3}]]&/@ DateRange[ {2024,1,1},{2024,12,31}],PrimeQ] (* Harvey P. Dale, Sep 01 2023 *)