To date, many generalized Fermat primes have been discovered. However, few people have considered this question: if the base b and the exponent n are such that b^2^n+1 is prime, is it possible for the result to remain prime if b is kept constant while the value of n is changed? In other words, does there exist a base b of a certain size such that combinations of b with multiple distinct exponents n all yield prime numbers? Thus, the new project was born. We raise the larger bases of those generalized Fermat primes with small exponents to higher exponents and test the primality of the resulting new numbers. This process is feasible because, in a traditional sequential search, the computational time increases with the exponent; consequently, over the course of many years, the upper bound for the base associated with a large exponent becomes significantly lower than that for a base associated with a small exponent. We will test these bases to see if we are lucky enough to discover new prime numbers. The project IBGFPS (Identical Base Generalized Fermat Prime Search) will go live tonight.
迄今为止，人们已经发现了许多广义费马质数。但是，很少有人关注到这样一件事：如果底数b和指数n使得b^2^n+1是质数，那么保持b不变，改变n的值，还有可能是质数吗？换言之，是否存在一定大小的底数b，使得b与多个不同的指数n的组合都是质数？该新项目由此诞生。我们将那些小指数的广义费马质数的更大底数带入更高的指数，测试新的数的素性。这一过程能够实现，是因为在传统的顺序搜索中，指数越大，计算时间越长，因此多年累积下，测试底数的上界就比小指数对应底数的上界小了很多。我们将测试这些底数，看看是否有足够的运气发现新的素数。项目IBGFPS (Identical Base Generalized Fermat Prime Search)将于今晚上线。