New prime generating quadratic polynomials

In 1772 Euler introduced the prime – generating quadratic polynomial of the form P (n) = n² - n + 41 The simplest forms of another kind of Eulerian prime generating quadratic polynomials of a type P(n) = n² - n + 1, n = 1,2,3,4,6,7,8,9, … and P(n) = n² + n – 1, for n = 2,3,4,5,6,8,9,10,11, … are first considered. Introduction.

1772年，欧拉（Euler）提出了形如$P(n) = n^2 - n + 41$的素数生成二次多项式。本文首先研究了另一类欧拉型素数生成二次多项式的最简形式：$P(n) = n^2 - n + 1$（对应$n$的取值为1,2,3,4,6,7,8,9,…）与$P(n) = n^2 + n - 1$（对应$n$的取值为2,3,4,5,6,8,9,10,11,…）。引言。