8053
This number is a prime.
Prime 8053 has an unusual property: every (non-null) permutation of its digits, excepting those that produce a leading zero, is a composite number: 8503 = 11 x 773, 5803 = 7 x 829, 5083 = 13 x 17 x 23, and all the others are obviously divisible by either 2 or 5. Even more remarkably, there is only one larger prime (the next one, 8059) with this property. [Keith]
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