Repartition of smooth integers under additive constraints.

Adrien Mounier

Date(s) : 08/06/2023   iCal
17 h 00 min - 18 h 00 min

It is known by everyone that it’s difficult to efficiently compute the factorization of a big integer in general. However, it becomes easy when this integer has only small prime divisors. Those integers are called smooth (or sometimes friable) and they have been of a particular interest in the 80’s because of their application in cryptography.
As it is the case with prime numbers, we would like to know how they behave under additive constraint but one can intuit that it is a difficult problem to deal with because in the case of primes, this kind of question is a rich source of unsolved problems like the famous Golbach or twin primes conjectures.
However, it is possible to find a lower bound for the set of smooth integers such that their successor is also smooth. We will also see a beautiful result which is true under the Elliot-Halberstam conjecture for smooth integers.



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