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A327914
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The 58 prime dates of each non-leap year of the form concatenate(month,day) with leading zero for days 1..9.
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7
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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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).
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KEYWORD
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nonn,easy,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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