User talk:140.112.212.54

In the article, it says: "By the way, when the maximum prime factors of p-1 for each prime factors p of n are all the same in some rare cases, this algorithm will fail."

I found this claim to be interesting but have been unable to come up with an example that demonstrates it.

1. I'm not quite sure in what way the algorithm "fails" when appropriate primes are used.

2. If found some primes which meet the criteria but the algorithm is successful.

p = 15217, p-1=2*3*5*509 q = 21379, q-1=2*3*7*509 r = 39703, r-1=2*3*13*509

The maximum prime factors of p-1, q-1 and r-1 are all 509.

When n= the product of any pair of p,q,r or the product of all three, the algorithm succeeds.

I started with an exponent e=509! and a=2.

For example,

n=p*q*r a = 2; e = 509! = ... 5^125 * 7^83 * 13^42 ... ep = e/5^125 // p-1 doesn't divide ep but q-1 and r-1 do divide ep

pollard(n,a,ep) produces gcd=848810437 = 21379 * 39703 as expected. With n= product of any pair of p,q,r, I also get success with the algorithm.

Would you please provide an example n that demonstrates your claim?

WrongTrousers (talk) 16:32, 28 March 2019 (UTC)