Developing math vocabulary
Prime Number
Pronunciation: PRYME NUM-ber
A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.
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Plain language
What it means
A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.
Formal meaning
Mathematical definition
An integer p > 1 is prime when its only positive divisors are 1 and p.
Where it fits
Its place in mathematics
Prime numbers are the basic multiplicative building blocks of positive integers.
Why it matters
The practical reason to learn it
They support factoring, fractions, modular arithmetic, number theory, and modern cryptography.
Worked example
Test a number for primality
Determine whether the whole number 29 is prime.
- Test divisibility by primes no greater than the square root of 29.
- Check 2, 3, and 5. None divides 29 evenly.
29 is prime.
Real-life example
Where this appears
A cybersecurity engineer uses large primes in public-key cryptographic systems.
Common mistake
What to watch for
Calling 1 prime. It has only one positive factor, so it does not meet the exactly-two-factors definition.
Memory tip
Keep this in mind
To test a number, check possible prime divisors only up to its square root.
Little-known fact
Keep curiosity alive
Euclid proved that there are infinitely many prime numbers.
A profession that uses this idea
Prime numbers help protect information
Cryptographic systems use difficult factorization problems built from large prime numbers.
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Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
Euclid
The author traditionally associated with the Elements, a systematic presentation of definitions, postulates, proofs, geometry, and number theory.
Eratosthenes
Eratosthenes was mathematician, geographer, and librarian. He estimated Earth’s circumference from shadow angles and created a sieve for identifying prime numbers.
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