Problems & Puzzles: Puzzles

Puzzle 1206 Follow-up to Puzzle 16

Puzzle 16 asks for the first k consecutive primes ending in the digit d

In may 4, 2020, Jan van Delden found that:

Ending digit 7 Length: 17 Start prime: 101684513099627

Ending digit 9 Length: 17 Start prime: 71894236537009

Q. For k=17 find the corresponding start prime for d=1 and for d=3.


From Feb. 1 to 7, 2025 contributions came from Giorgos Kalogeropoulos, Michael Branicky,

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Giorgos wrote:

All these numbers have been known since 2013 from Giovanni Resta's work.
Here are the OEIS links for each digit

d=1, up to k=19  --->  https://oeis.org/A057618
d=3, up to k=19  --->  https://oeis.org/A057631
d=7, up to k=18  --->  https://oeis.org/A068150
d=9, up to k=17  --->  https://oeis.org/A057636

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Michael wrote:

These answers and further extensions to Puzzle 16 are in the OEIS.
d=1 is OEIS A057618 and k=17..19 are there: 253931039382791, 253931039382791, 253931039382791
d=3 is OEIS A057631 and k=17..19 are there: 269013937530553, 281659318133953, 281659318133953
d=7 is OEIS A068150 and k=18 is there: 196948379177587
d=9 is OEIS A057636 but stops at k=17

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