Number Theory quiz

More questions about Number Theory

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   Why is the number 1 not considered a prime number by mathematicians?

   Answer: It has only one factor

   Why: Printed prime tables still began with one as late as 1956, and leaving it out is what makes every number's factorization unique.

2. 2 Medium

   What integer has proper divisors that sum to more than itself?

   Answer: Abundant number

   Why: The smallest is 12, whose divisors 1, 2, 3, 4 and 6 total 16, and the first odd example, 945, follows 231 even ones.

3. 3 Hard

   Which form do most record-breaking prime numbers take?

   Answer: $2^n - 1$

   Why: Mersenne primes, named for the French friar Marin Mersenne, still hold the record: the 2024 find runs to 41,024,320 digits.

4. 4 Easy

   What is an integer that leaves a remainder of 1 when divided by 2 called?

   Answer: Odd number

   Why: Adding any two odd numbers always produces an even number, whereas multiplying them always results in another odd number.

5. 5 Medium

   Under Benford's Law, which digit is the most common leading number?

   Answer: 1

   Why: In many real world data sets this digit leads about 30 percent of the time; Simon Newcomb noticed it in 1881 in worn logarithm tables.

6. 6 Hard

   If $p$ and $2p+1$ are both prime, $p$ is which type?

   Answer: Sophie Germain prime

   Why: Germain wrote to Gauss under the pen name Monsieur Le Blanc; the larger partner prime is called a safe prime and shields key exchange.