89

This number is a prime.

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The larger of only two double-digit primes that does not produce a prime by adding a digit to it. (There is no prime "89d"). The smaller such prime is 53. [Loungrides]

The smallest prime that can be written as sum of two powers in five ways. [Loungrides]

The only prime of form p^4+8 for p a prime, (p=3). [Loungrides]

The only double-digit prime that can be written as p*q+r in seven ways, where p, q, r are distinct primes, i.e., 89 = 2*3+83 = 2*5+79 = 2*11+67 = 2*23+43 = 2*29+31 = 2*41+7 = 2*43+3. [Loungrides]

The only non titanic prime of form n!-n#-1, (n=5). [Loungrides]