 210 (another Prime Pages' Curiosity) Curios: Curios Search:   Participate:  GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits) The primes 47, 257, 467, 677, 887, 1097 and 1307 constitute a progression of 7 terms with a common difference of 210. [Barrow , Bush and Taylor] 210 is the smallest number with 4 distinct prime divisors. The largest single-digit primorial value (7# = 2 * 3 * 5 * 7 = 210). [Nicholson] It has been estimated that 210 becomes a "jumping champion" at around 10^425. (21, 20, 29) and (35, 12, 37) are the two least primitive Pythagorean triangles with different hypotenuses and the same area (=210). [Sierpinski] The number of distinct representations of a number n as the sum of two primes is at most the number of primes in the interval [n/2, n-2], and 210 is the largest value of n for which this upper bound is attained. In other words, 210 is the largest positive integer n that can be written as the sum of two primes in (n - 2) - (n/2 - 1) distinct ways. Reference: An upper bound in Goldbach's problem. [Capelle] 210^k+1 is prime for k = 2, 1, 0. [Bajpai] Bergot's Problem: Let p,q,r be three consecutive primes and note that |101^2-97*103| = 7# = 210. Does there exist another solution p,q,r |q^2-p*r| that equals a larger primorial? C(10,4) = 2*3*5*7 = 7# = 210, i.e., the number of combinations of 10 objects taken 4 at a time is a primorial. Does there exist a larger example that ignores C(n,1) and C(n,n-1)? [Honaker] (There is one curio for this number that has not yet been approved by an editor.)   To link to this page use /curios/page.php?number_id=49 Prime Curios! © 2000-2019 (all rights reserved)  privacy statement   (This page was generated in 0.0131 seconds.)