Exercise 555Number theory › PrimesHigh schoolAdded 3 Nov 2026

Trial division primality test

#trial division#primality test#algorithm

Statement

Test whether $127$ is prime using trial division.

Hint

Test divisibility by primes up to $\sqrt{127}\approx11.3$ .

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Solution

Primes to test. $2,3,5,7,11$ .

Divisibility.
- $2$ : $127$ odd, no.
- $3$ : $1+2+7=10$ , not divisible by $3$ .
- $5$ : ends in $7$ , no.
- $7$ : $127=7\cdot18+1$ , no.
- $11$ : alternating sum $7-2+1=6$ , not $0$ , no.

Conclusion. $127$ is prime.

Trial division primality test

Statement

Solution

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