101

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This article is about a particular natural number.|View all articles on particular natural numbers

Summary

Factorization

The number 101 is a prime number.

Polynomials

Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 101 for suitable input choice.

Polynomial Degree Some values for which it generates primes Input value at which it generates 101
2 all numbers 1-10, because 11 is one of the lucky numbers of Euler. 10
2 all numbers 0-28 6

Irreducible polynomials by Cohn's irreducibility criterion

By Cohn's irreducibility criterion, we know that if we write 101 in any base greater than or equal to 2, the corresponding polynomial is irreducible. We list here the irreducible polynomials of this type that are of degree at least two:

Base 101 in base Corresponding irreducible polynomial
2 1100101
3 10202
4 1211
5 401
6 245
7 203
8 145
9 122
10 101