论文标题
明确的上限，用于同时由任何一组不可约多项式表示的素数的数量
Explicit upper bounds for the number of primes simultaneously representable by any set of irreducible polynomials
论文作者
论文摘要
使用Selberg上筛的明确版本，我们获得了$ n \ leq x $数量的明确上限，以使一组不可约多的多项式$ f_i（n）具有整数系数同时使用。该组可以根据需要包含任意多的多项式。为了证明，我们介绍了一些不可约多项式的计算，并获得了高达$ x $的Sophie Germain Prime数量的明确上限，这些索菲（Sophie Germain）数量最高为$ x $，这些数量在加密术中具有实际应用。
Using an explicit version of Selberg's upper sieve, we obtain explicit upper bounds for the number of $n\leq x$ such that a non-empty set of irreducible polynomials $F_i(n)$ with integer coefficients are simultaneously prime; this set can contain as many polynomials as desired. To demonstrate, we present computations for some irreducible polynomials and obtain an explicit upper bound for the number of Sophie Germain primes up to $x$, which have practical applications in cryptography.
