Maths WorkshopMaths problems with full solutions
Exercise 264Number theory › PrimesHigh schoolAdded 3 Nov 2026

Definition and first examples of primes

#primes#definition#examples

Statement

A prime number is an integer p≥2p\ge2 whose only positive divisors are 11 and pp. List all primes less than 5050 and justify that 9191 is not prime.

Hint

For 9191, test divisors up to 91≈9.5\sqrt{91}\approx9.5.

Show solutionHide solution

Solution

Primes under 5050. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,472,3,5,7,11,13,17,19,23,29,31,37,41,43,47.

9191 is not prime. 91=7⋅1391=7\cdot13, both factors between 22 and 9090. Alternatively, 91=7⋅1391=7\cdot13 directly.

Conclusion. There are 1515 primes less than 5050, and 9191 is composite.