Problems & Puzzles: Puzzles

 Puzzle 948. Vampire numbers again Carlos Rivera asks for a PVN* (Prime Vampire Number) equal to the square of a palprime. Rivera's best approach is a VN = 3191569913965884999654819334486225 = (56493981218939465)^2. This is not a PVN but just a VN because the squared integer is a palindrome, not a palprime. Q. Send your smallest solution (and three more if possible)? ______ * See Puzzle 199

Contribution came from Giovanni Resta

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Giovanni wrote on April 8, 2019:

I did not find any solution with less than 23 digits.

Those with 23 digits are 17:

32154619780908791645123, 32384776915051967748323,
34209817561016571890243, 35719846200200264891753,
36684105759295750148663, 37621418905050981412673,
39247586140304168574293, 70319484952625948491307,
72409515396869351590427, 75246289003030098264257,
76202514389798341520267, 76524913880408831942567,
77912854360606345821977, 79205831946264913850297,
90147518626362681574109, 90538542761116724583509,
96541303927372930314569.

the first such prime palindromes with 25 digits are:

3205189677447447769815023, 3276874035190915304786723,
3281076045919195406701823,

and the first with 27 digits are:

316580942302717203249085613, 316589254580727085452985613,
317293609058454850906392713.

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