127

This number is a prime.

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The smallest of only two primes less than a googol of form 5^x+2, where x is a prime (case x=3). The largest such prime less than a googol is for x=17. [Loungrides]

The smallest Friedman prime. [Loungrides]

The smallest prime that is the arithmetic average of four consecutive primes, i.e., 113, 127, 131, 137. [Loungrides]

127 is the 15th Fibonacci 7-step (heptanacci) number. Note that 2^7-1 = 127, making it the 4th Mersenne prime. [Loungrides]

The smallest prime de Polygnac number. [Loungrides]