A prime number p with n digits is called an embedded prime if it remains prime after eliminating the leftmost i digits of p, for i = 0,...,n-1. For example:
137 is an embedded prime because
-137 is prime
-37 is prime
-7 is prime
or
45197 is an embedded prime because
-45197 is prime
-5197 is prime
-197 is prime
-97 is prime
-7 is prime
But, 4127 is not an embedded prime because
-4127 is prime
-127 is prime
-27 is NOT prime
-7 is prime
Is the set of all embedded primes infinite? If not, what is the largest embedded prime? If there is a largest, then since any n digit embedded prime is an extension of an n-1 digit embedded prime, this question seems suitable to be answered by a computer program. However, I have neither the means nor know-how to experiment.
2006-07-06
06:28:36
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7 answers
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asked by
Anonymous