Its clear that there is about 15 years (2004-2019) after the publication of AKS primality testing in 2002 and its modifications in 2003-2004. AS result, is there any development happened in this theory after 2004 ?
Dear Ramez Hindi
Many results appeared every day; all that you need is to followup on the published articles. That required access that allows you to see all the updates.
As of November 2017, the largest discovered prime was in November 2017
using the ECPP ( elliptic curves primality tests ) method. It has 34,987 digits.
It takes 756 days to test the primality of 2116224- 15905.
See
Caldwell, Chris. The Top Twenty: Elliptic Curve Primality Proof from the Prime Pages.
Best wishes
Thank you Professor , i like to support us with few references may help me to follow that project with open access !
This is a book from 2009 on the topic: https://link.springer.com/book/10.1007/978-0-387-77268-4#authorsandaffiliationsbook
As far as I know this is the latest (public) result on progress in factoring:
https://arstechnica.com/information-technology/2019/12/new-crypto-cracking-record-reached-with-less-help-than-usual-from-moores-law/
There is no significant algorithmic advance in this work though.
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