I have been doing some manual sieving and thought that it found the numbers that would most likely be primes. Well I asked the question on the Primegrid forum and the Project Scientist informed me that was absolutely wrong as the sieveinf ound numbers that were not Primes.

My Question:

What is the meaning of the two numbers of Manual Sieving. Is Sieving finding numbers that might be Prime ?

959815134871698800641 | 709500654^2097152+1

959815195922830196737 | 802617394^2097152+1

A layman's answer if possible.

Ravi Fernando, Project scientist, gave me the following answer.

It's the opposite: sieving identifies numbers that definitely aren't prime, because they have nontrivial factors. The vertical bar symbol "|" means "divides", or in normal English "is a factor of". So what you wrote says that the two GFN-21 numbers on the right, each with over 18 million digits, are multiples of the 21-digit numbers on the left, and in particular can't be prime. This saves us the work of testing the 18-million-digit numbers further.

Related thread: here.

[/size]