A327349 The 67 prime dates in each leap year of the form concatenate (month,day) without leading zeros for days.

11, 13, 17, 19, 113, 127, 131, 23, 29, 211, 223, 227, 229, 31, 37, 311, 313, 317, 331, 41, 43, 47, 419, 421, 53, 59, 521, 523, 61, 67, 613, 617, 619, 71, 73, 79, 719, 727, 83, 89, 811, 821, 823, 827, 829, 97, 911, 919, 929, 101, 103, 107, 109, 1013, 1019, 1021, 1031, 113, 1117, 1123, 1129, 127, 1213, 1217, 1223, 1229, 1231

Offset: 1

Author

Wolfdieter Lang, Sep 30 2019

Keywords

• nonn
• easy
• fini
• full

Comments

In a leap year the months 1, 2, ..., 12 contribute 7, 6, 6, 5, 4, 5, 5, 7, 4, 8, 4, 6 such dates. This adds to 67 prime dates. For non-leap years see the 66 prime dates given in A327348.

Crossrefs

Cf. A327346 (74 prime dates of the form d.m (no leading 0's for m and d)), A327347 (55 prime dates of the form d.m with leading 0's for m = 1, 3, 7, 9), A327348 (non-leap year case), A327914 (58 prime dates of the form m.d in non-leap years, with leading 0 for d = 1..9), A327915 (59 prime dates like A327914 but for leap years).

Programs

Mathematica

Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[Join[m, IntegerDigits[#]]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 29, True, 31]} &, 12], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)