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Old 2008-10-27, 02:33   #5
Jens K Andersen
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Feb 2006

23010 Posts

Originally Posted by Oleg V.Cat View Post
First digit is a prime.
Intresting, that digits "1" and "7" are rare.
You appear to include 1 in the primes. This is rarely done today. If 1 is not considered prime then we get the right-truncatable primes in A024770. There are 83 in total and the largest is 73939133.

Your 4099339193933 is listed at My submitted numbers included 133028062963 which is the smallest prime where a prime-making digit can be appended 14 times, ending with 13302806296379339933399333. Can you find a 15?

The many 3's and 9's is no coincidence. Appending 3 or 9 to a decimal number does not change the value modulo 3. But appending 1 or 7 increases the value modulo 3 by 1. If it was 2 before then it becomes 3 (or congruently 0) and thus divisible by 3. If it was 1 then it becomes 2, and will become divisible by 3 next time a 1 or 7 is appended. So at most two 1's or 7's in total can be appended.

My website has another variation at where two decimal digits are appended at a time. Let p110 =
p110 gives 55 primes after 2, 4, 6, ..., 110 digits. An exhaustive search showed this is maximal for primes starting with 11. Exhaustive searches for all other starts would be feasible but take longer than I'm willing to do.
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