719

This number is a prime.

+ The largest prime p less than 1000 such that e^(π*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 Smarandache-Wellin prime if concatenated in increasing order.

+ The smallest factorial prime of the form n!-1 such that n-1 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 n-by-n-by ... by-n array of primes, where each line of n primes parallel to any edge is an arithmetic progression. The largest prime in the smallest 3-by-3-by-3 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
[Granville]

+ The number of days that have elapsed between the discovery of the 44th and 45th Mersenne primes. [Vrba]

+ The largest odd highly-imperfect 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 3-digit distinct-digit 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]

+ Operation Lam Son 719 was a limited-objective offensive campaign conducted in the Kingdom of Laos. The primary objective was to destroy supply dumps and sever the Ho Chi Minh Trail, the logistical corridor running through eastern Laos from North Vietnam south to Cambodia. [Napier]

+ 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 family-farmed winery in California.

+ The first occurrence of three consecutive multidigit prime values y0 of the fundamental solution pair (x0, y0) to Pellian x2 - Dy2 = 1 corresponding to prime values D as well: 5169602 - 516959*7192 = 1 ; 5285282 - 528527*7272 = 1 ; 5372882 - 537287*7332 = 1. [Beedassy]

+ The number of original cast performances of the 1961 musical Carnival. [Pyne]

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