Primes p > 3; p||p||p/(p*p) is prime?

|| is the symbol for concatenation.

Concatenation is the joining of two numbers by their numerals. That is, the concatenation of 123 and 456 is 123456.

The prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, …
http://oeis.org/A000040

We start with 666/6*6 = 37/2

The 6-th prime number is 13
Replacing the three 6 digits with the 6-th prime or 13, we get

131313/(13*13) = 777

We go from one Repdigit number, 666, to produce another Repdigit number, 777.
http://en.wikipedia.org/wiki/Repdigit

And 37:     373737/(37*37) = 273 (= 3*7*13)

The 37-th prime number is 157

157157157 / (157*157) = 1001001/157 = 6375.80254….

222/(2*2) = 111/2 = 55.5

The 2-nd prime number is 3: 333/(3*3) = 37 (the 12-th prime)

With 7:     777/(7*7) = 111/7 = 15.8571

The 7-th prime is 17:    171717(17*17) = 49626213 (= 3 * 7 * 13 * 17^3 * 37)

Question: Can you find a prime p > 3; p||p||p / (p*p) is prime?

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About benvitalis

math grad - Interest: Number theory
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