Please help in finding the factor of ...618240007109027021 by the p-1 method...
thanks a lot!
n = 618240007109027021
Select a bound for the factorial.
bound = $\displaystyle \ln(n)$ is an acceptable limit.
In this case about 43 .
The exponent will be 43! (factorial of 43)
Choose some number to raise to that exponential value. Any number (a) from 2 to n-1 is useable.
You may want to check that $\displaystyle \gcd(a,n)=1$.
2 is ok.
$\displaystyle r = ( 2^{43!}\mod n )$
$\displaystyle f = \gcd(r-1,n)$
If
$\displaystyle 1<f<n$
then you have a factor of n
If not then raise the bound limit.
In this case one of the factors is a 9 digit number.
The first 3 digits and the last 3 digits are
250___201
.