prime numerzzz..
Number Theory
Level
3
Find the smallest prime whose reversal is composite and the smallest invertible prime.
Details and assumptions :
The answer of both the question is same, if you think number does not exist then enter 0.
The answer is 19.
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1 solution
An invertible prime must contain only 1,6,8,9 as digits. Invertible primes are 11 (whose inverse is 11 itself), 19 (whose inverse is the prime 61), 61 (whose inverse is 19), 101 (whose inverse is 101), 109 (whose inverse is the prime 601) and so on. I just noticed that the reversal of 61 is 16 (that is composite) so I just checked 19 and 11 to determine if they are lower than 61 and satisfy the condition that the reversal is composite. While the reversal of 11 is 11 (is still a prime, not composite) and the reversal of 19 is 91 (not a prime since 7 divides it) the answer is 19.