2012/07/31 by Justin DeBenedetto, Jeremy Rouse, DeBenedetto, Justin +1
Computer Science · Mathematics · #11Y11 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11Y11
paper · pdf · doi:10.48550/arxiv.1207.7291
6 pages
arxiv created 2012/07/31 · openalex publication_date 2012/07/31 · arxiv updated 2012/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by Euler's observation that the polynomial x2 + x + 41 takes on prime values for 0 ≤ x ≤ 39, we search for large values of x for which N = x2 + x + 41 is prime. To apply classical primality proving results based on the factorization of N-1, we choose x to have the form g(y), chosen so that g(y)2 + g(y) + 40 is reducible. Our main result is an explicit, 60,000 digit prime number of the form x2 + x + 41.