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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

Just showing those entries submitted by 'Rupinski': (Click here to show all)

Jason Funk © 2002
+ In the fifth and all higher dimensions there are only 3 regular polytopes. [Rupinski]

+ The greatest number of consecutive integers which are pairwise relatively prime. [Rupinski]

+ The function n^(1/n) achieves its maximum value for integers n at n = 3. [Rupinski]

+ According to the quadratic reciprocity theorem, if p and q are distinct primes of the form 4k+3, then exactly one of the following congruences is solvable in integers: x^2 = p mod q or x^2 = q mod p. [Rupinski]

+ The only Sophie Germain Prime p of the form 4k+3 such that Mp is prime. All larger Mp for such p are composite as shown by Euler and Lagrange. [Rupinski]

+ The smallest possible Proth prime, k*2n+1 with k < 2n, here k=1, n=1. [Rupinski]

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