The RGFP-P_19=(1721592*P18)^2+1 —or, written out in full:

`(1721592*(((124812*(((599098*(((135704*(((25370*(((50352*(((58764*(((2380*(((1680*(((5010*(((1056*(((1870*(((170*(((60*(((2*(((96*(((10*(((2*(((2*(1))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1`

—is a prime number (proved by pfgw64), and the smallest P_19 prime.

RGFP-P_19=(1721592*P18)^2+1 ，或者

`(1721592*(((124812*(((599098*(((135704*(((25370*(((50352*(((58764*(((2380*(((1680*(((5010*(((1056*(((1870*(((170*(((60*(((2*(((96*(((10*(((2*(((2*(1))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1)))^2+1`

是一个质数（由pfgw64证明），也是最小的P19质数。