691

This number is a prime.

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The smallest prime that can be written as the sum of thirteen consecutive primes. Recall that 691 is thirteen squared, turned upside down. [Post]

The number of prime unlabeled topologies (i.e., prime homeomorphism classes) on 6 points, and the largest known prime of that form. [Post]

The smallest prime coefficient in the the minimal resolution of the Sylow 2-subgroup of the Mathieu group M24 out to degree 13: the Poincare series being 1 + 4t + 12t^2 + 25t^3 + 49t^4 + 85t^5 + 143t^6 + 222t^7 + 336t^8 + 485t^9 + 691t^10 + 953t^11 + 1298t^12 + 1726t^13 + O(t^14). [Post]