A biprime is a positive integer that is the product of precisely two (not necessarily distinct) primes. A cluster of biprimes is an ordered triple (m, m+1, m+2) of consecutive integers that are biprimes. There are precisely three clusters of biprimes below 100. Denote these by, say,
\{(p, p+1, p+2),(q, q+1, q+2),(r, r+1, r+2)\}
and add the condition that p+2<q<r-2 to fix the three clusters. Interestingly, p+1 and q are both multiples of 17. Concatenate q with p+1 in that order, and write down the result.
\{(p, p+1, p+2),(q, q+1, q+2),(r, r+1, r+2)\}
and add the condition that p+2<q<r-2 to fix the three clusters. Interestingly, p+1 and q are both multiples of 17. Concatenate q with p+1 in that order, and write down the result.