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PUZZLET 190

Count the Days for Palindromic Primes

Beginning at the end of January 2000, a mathematician totalises the days in the month just over. He does this every month thereafter, adding the new monthly total onto the current total. The totals accumulate to generate the series 31, 60, 91, 121, 152 ...

calendar

mathematician
Assuming he lives long enough, when will he see a total that is also a palindromic prime number? How many times this century?  When will the next one occur after this century? Note that leap years must be taken into consideration.


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