A327914 The 58 prime dates of each non-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, 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, 907, 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

All these dates come in non-leap years from the months January, February, ..., December, in the form m.d, with a 0 in front of the days 1..9, with 7, 3, 5, 4, 4, 5, 4, 6, 4, 5, 5, 6 prime dates, respectively, adding up to 58. For the corresponding leap year case with 59 prime dates see A327915.

Comparing with A327914 (no leap year, no 0 in front of days d = 1..9) one finds the number differences for the months 0, -2, -1, -2+1 = -1, 0, 0, -1, -1, -1+1 = 0, -3, +1, -1+1 = 0, respectively. For a month with difference 0 (Jan, May, Jun) one just has to add a zero before the days 1..9 in A327914. In the other cases a -x indicates that x dates are no longer prime after insertion of a 0 before days 1..9, and +1 indicates that a new prime date appears: Feb: 203 and 209 out, Mar: 301 out, Apr: 403 and 407 out, 409 in, Jul: 703 out, Aug: 803 out, Sep: 907 out, 901 in, Oct 101, 103 and 107 out, Nov: 1109 in, Dec: 1207 out, 1201 in.

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), A327915 (59 prime dates, for 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, 28, 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[ {2023,1,1},{2023,12,31}],PrimeQ] (* Harvey P. Dale, Sep 01 2023 *)

Extensions

a(39) corrected by Seth A. Troisi, May 18 2022