yaworsw/euler-manager

---
:id: 288
:name: An enormous factorial
:url: https://projecteuler.net/problem=288
:content: "For any prime <var>p</var> the number N(<var>p</var>,<var>q</var>) is defined
  by N(<var>p</var>,<var>q</var>) = ∑<sub><var>n</var>=0 to <var>q</var></sub> T<sub><var>n</var></sub>\\*<var>p</var><sup><var>n</var></sup>
  \ \n with T<sub><var>n</var></sub> generated by the following random number generator:\n\nS<sub>0</sub>
  = 290797  \nS<sub><var>n</var>+1</sub> = S<sub><var>n</var></sub><sup>2</sup> mod
  50515093  \nT<sub><var>n</var></sub> = S<sub><var>n</var></sub> mod <var>p</var>\n\nLet
  Nfac(<var>p</var>,<var>q</var>) be the factorial of N(<var>p</var>,<var>q</var>).
  \ \nLet NF(<var>p</var>,<var>q</var>) be the number of factors <var>p</var> in Nfac(<var>p</var>,<var>q</var>).\n\nYou
  are given that NF(3,10000) mod 3<sup>20</sup>=624955285.\n\nFind NF(61,10<sup>7</sup>)
  mod 61<sup>10</sup>\n\n"