Prime Curios!: 216

216
(another Prime Pages' Curiosity)

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Zhi-Wei Sun conjectured in March 2008 that 216 is the only number not of the form p + k(k+1)/2, with p = 0 or p prime. [Hasler]

The numbers 6*216+1, 12*216+1, and 18*216+1 are all prime and hence their product is Carmichael. [Patterson]

The number of decompositions of 216 into integer summands without regard to order is prime (15285151248481). [Patterson]

216 is the smallest number that may be expressed as the difference of the sums of the squares of successive twin primes (13^2 + 11^2) - (7^2 + 5^2). [King]

The smallest untouchable number which is a cube. [Gupta]

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