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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) ZhiWei 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] The smallest and only known cube sandwiched between two triplets of semiprimes (i.e., 213=3*71, 214=2*107, 215=5*43 and 217=7*31, 218=2*109, 219=3*73). [Gupta]
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