The book is now available! 719
(another Prime Pages' Curiosity)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ The largest prime p less than 1000 such that e^(pi*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]

+ 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.

(There are 2 curios for this number that have not yet been approved by an editor.)

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