Problem 981. Find nearest prime number less than input number

Created by Reza Ahmadzadeh

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Find nearest prime number less than input number.

For example: if the input number is 125, then the nearest prime number which is less than this number is 113.

Be careful, in that 1 is not a prime number. So there is NO prime less than 2.

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Last Solution submitted on May 06, 2025

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@bmtran (Bryant Tran) on 10 Oct 2012

1 isn't a prime number

Disha on 31 Jul 2013

agree @bmtran...

Grzegorz Knor on 20 Sep 2013

You should correct the test suite. 1 isn't a prime number.

Vishal on 6 Oct 2014

Correct the test suite 1 is not prime number.

Daniel Pereira on 6 May 2016

1 is not a prime number, in order to fulfill with the fundamental theorem of arithmetic:

https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

https://en.wikipedia.org/wiki/Prime_number#Primality_of_one

John D'Errico on 22 Feb 2018

I removed the test case where n==2, since 1 is indeed not a prime number. I also added a random test case, so the problem is not so easily cooked by knowing all the test cases.

Brandon on 30 May 2023

1 is indeed prime. Aliens will laugh at us when we say it is not. 1 causes all sorts of problems by not being prime. As many as it causes by being prime. It is already an exception in thousands of mathematical theorems. Why mathematicians chose this one theorem to not include 1 as an exception is beyond me.

Christian Schröder on 31 May 2023

1 is a unit (in the ring-theoretic sense), and units are excluded from the definitions of prime elements and irreducible elements in rings. I'm not a mathematician and don't have more than a basic undergrad exposure to abstract rings, but there surely is a good reason. Any mathematicians reading this who can shed on light on this?

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Problem 981. Find nearest prime number less than input number

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Problem 981. Find nearest prime number less than input number

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