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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest prime p less than 1000 such that e^(*sqrt(p)) differs from an integer by less than 0.0001. [Rupinski] A number that can be expressed as both a factorial prime (6!  1) and as an abundant number less one. [Patterson] The first consecutive primes up to 719 will form a SmarandacheWellin prime if concatenated in increasing order. The smallest factorial prime of the form n!1 such that n1 is a factorial prime of the same form. [Capelle] The number of rooted trees with 10 nodes and also the number of ways of arranging 9 nonoverlapping circles. [Beedassy] The hour and second hands of an analog clock align exactly 719 times every twelve hours. [Rosulek] A Balog cube is an nbynby ... byn array of primes, where each line of n primes parallel to any edge is an arithmetic progression. The largest prime in the smallest 3by3by3 cube is 719. 47 383 719 149 401 653 251 419 587 179 431 683 173 347 521 167 263 359 311 479 647 197 293 389 83 107 131 The number of days that have elapsed between the discovery of the 44th and 45th Mersenne primes. [Vrba] The largest odd highlyimperfect number, which sets a record for the value of sigma(n)2n, is a(79) = 719. Both 79 and 719 are prime. [Post] The largest 3digit distinctdigit prime that remains prime if any of its digits is removed. [Loungrides] The first 719 positive values of n are composite for n^4 + 179. [Homewood] The prime number 719 can be written as the sum of terms k!k for k = 1, ... ,5 with k an integer. [Sandri] The sum of the first 13670 prime numbers is the reverse cube 959496173 = reversal of 719^3. [Gaydos] 719 West Cellars is part of a familyfarmed winery in California.
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