1,1

For the numbers for leap years see A327919.

Only the months February (2), March (3), May (5), July (7) and November (11) qualify. The qualifying prime days are for month m=2: 3, 5, 7, 11, 13, 17, 19, 23; for month m = 11: 3, 5, 7, 11, 13, 17, 19, 23, 29 and for months m = 3, 5, and 7: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.

The months m = 2, 3, 5, 7, 11 contribute 3, 5, 2, 2, 4 days, respectively, adding to 16.

FromDigits[Flatten[IntegerDigits/@#]]&/@(Select[{#[[2]], #[[3]]}&/@DateRange[{2021, 1, 1}, {2021, 12, 31}], AllTrue[#, PrimeQ && PrimeQ[ FromDigits[ Flatten[ IntegerDigits/@#]]]]&]) (* Harvey P. Dale, Nov 16 2025 *)

Cf. A165243 (first three terms), A165292 (first five terms), A165555 (first two terms), A167187 (first two terms), A327348 (m and d nonprime allowed), A327914 (with 0 before d = 1..9), A327919 (leap year), A327920 (pure prime dates of d.m form).

Sequence in context: A263521 A084428 A322287 * A327919 A165243 A142374

Adjacent sequences: A327915 A327916 A327917 * A327919 A327920 A327921

nonn,easy,fini,full

Wolfdieter Lang, Oct 08 2019

approved