  Translated from the Latin original "Facillima methodus plurimos numeros
primos praemagnos inveniendi" (1778). E718 in the Enestrom index. If m is a
number of the form 4k+1 and is a sum of two relatively prime squares, then it
is prime if and only if it is not the sum of two other squares. In this paper
Euler wants to generalize this criterion. He looks at when 232aa+1 represents a
prime number. He uses his "numeri idonei" (suitable numbers, convenient
numbers, idoneal numbers).
