number theory
Prime — AMC & AIME Problems
67 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Prime — a number theory concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Prime Numbers — Definition & Examples, Primality Testing and Significance.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 8
AMC 10
- 2000 AMC 10 Problem 11
- 2002 AMC 10A Problem 14
- 2002 AMC 10A Problem 15
- 2002 AMC 10B Problem 6
- 2002 AMC 10B Problem 15
- 2003 AMC 10A Problem 14
- 2005 AMC 10A Problem 24
- 2005 AMC 10B Problem 12
- 2005 AMC 10B Problem 22
- 2013 AMC 10B Problem 24
- 2015 AMC 10B Problem 11
- 2018 AMC 10B Problem 5
- 2018 AMC 10B Problem 11
- 2019 AMC 10A Problem 9
- 2019 AMC 10A Problem 25
- 2019 AMC 10B Problem 2
- 2020 AMC 10B Problem 4
- 2021 AMC 10A Fall Problem 5
- 2021 AMC 10B Fall Problem 10
- 2022 AMC 10B Problem 6
- 2022 AMC 10B Problem 13
- 2024 AMC 10A Problem 3
AMC 12
- 1960 AMC 12 Problem 33
- 1969 AMC 12 Problem 23
- 1973 AMC 12 Problem 3
- 1973 AMC 12 Problem 18
- 1974 AMC 12 Problem 8
- 1975 AMC 12 Problem 22
- 1983 AMC 12 Problem 3
- 1999 AMC 12 Problem 4
- 2000 AMC 12 Problem 6
- 2002 AMC 12A Problem 12
- 2002 AMC 12A Problem 17
- 2002 AMC 12B Problem 3
- 2002 AMC 12B Problem 11
- 2005 AMC 12A Problem 18
- 2009 AMC 12B Problem 19
- 2010 AMC 12B Problem 25
- 2019 AMC 12A Problem 24
- 2019 AMC 12B Problem 2
- 2020 AMC 12B Problem 4
- 2021 AMC 12A Fall Problem 4
- 2022 AMC 12B Problem 3
More number theory concepts
- Chicken McNugget Theorem
- Chinese Remainder Theorem
- Continued fraction
- Digits
- Diophantine Equation
- Divisibility
- Euler’s Totient Function
- Factor
- Factor counting
- Fermat’s Little Theorem
- Greatest common divisor
- Least common multiple
- Legendre’s Formula
- Modular arithmetic
- Modular exponentiation
- Multiple
- Multiplicative order
- Palindrome
- Parity
- Perfect power
- Perfect square
- Power of 2
- Prime factorization
- Quadratic residue
- Sum of factors
- Trailing zeros
- Triangular number
- Units digit