523. The first three primes in a number which itself is prime and the only way a combination of the three could be prime.
Cool!
2357 and 2753 are both prime, so this can’t be extended by one more prime.
235,117 is prime, so is 257,311, five primes don’t work.
Seems fairly unlikely that there would be exactly one prime using 2, 3, 5, 7, 11 and 13, given there are 720 permutations.