Prime Numbers 1 to 100: List and How to Find Them

My Twirldrop record is 53 floors. And 53 has a superpower: it divides evenly only by 1 and by itself. It is a prime number, and I think that is way cooler than the record.

Here you get what a prime number is, the list from 1 to 100, an easy way to check if a number is prime and a few fun facts that even cicadas know.

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What is a prime number?

A prime number is a whole number greater than 1 with exactly two factors: 1 and itself. 7 is prime, because only 1 and 7 divide 7 with no remainder.

Numbers greater than 1 with more factors are called composite. 6 is composite, because 1, 2, 3 and 6 all divide 6.

List of prime numbers from 1 to 100

• 1 to 10: 2, 3, 5, 7
• 11 to 20: 11, 13, 17, 19
• 21 to 30: 23, 29
• 31 to 40: 31, 37
• 41 to 50: 41, 43, 47
• 51 to 60: 53, 59
• 61 to 70: 61, 67
• 71 to 80: 71, 73, 79
• 81 to 90: 83, 89
• 91 to 100: 97

There are 25 prime numbers between 1 and 100.

How to check if a number is prime

1. If the number is even and bigger than 2, it is not prime.
2. Add up the digits. If the sum is a multiple of 3, the number divides by 3. Example: 51, because 5 + 1 = 6.
3. If it ends in 0 or 5 and is bigger than 5, it divides by 5.
4. Try dividing by the primes 7, 11, 13 and so on, only up to the prime whose square is bigger than the number.
5. If none of them divides evenly, the number is prime.

Example with 91: it is not even, 9 + 1 = 10 is not a multiple of 3, and it does not end in 0 or 5. But 91 ÷ 7 = 13. So 91 is not prime, even though it looks like one.

The Sieve of Eratosthenes

More than 2,000 years ago, the Greek thinker Eratosthenes came up with a way to find every prime up to a number:

1. Write the numbers from 2 to 100.
2. Circle 2 and cross out all its multiples.
3. Circle the next number not crossed out, 3, and cross out its multiples.
4. Repeat with 5 and 7.
5. The numbers left uncrossed are the primes.

Prime factorization: every number is made of primes

Every number greater than 1 can be written as a product of primes in exactly one way. Example: 60 = 2 × 2 × 3 × 5 and 84 = 2 × 2 × 3 × 7.

That is why primes are called the building blocks of numbers.

Fun facts about prime numbers

• Primes never run out. The Greek mathematician Euclid proved it more than 2,000 years ago.
• Twin primes are pairs of primes 2 apart. Up to 100: 3 and 5; 5 and 7; 11 and 13; 17 and 19; 29 and 31; 41 and 43; 59 and 61; 71 and 73.
• Some periodical cicadas in the United States come out of the ground every 13 or 17 years, both prime numbers.
• Online shopping security relies on math with huge primes.
• The biggest known primes have tens of millions of digits and were found by computers.

A prime record in Twirldrop

In Twirldrop you spin a tower so the ball drops through the gaps, floor by floor. In the run in the picture, the screen shows 12 floors and a best of 53.

Polarzinho12 floors now, 53 as my best. 53 is prime. 12 is composite. I am an optimist.

Next prime after 53? 59. New goal unlocked.

FAQ

What are the prime numbers from 1 to 100?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Is 1 a prime number?

No. A prime needs exactly two factors, and 1 has only one.

What is the only even prime number?

2.

How many prime numbers are there?

Infinitely many. Between 1 and 100 there are 25.

Your turn

Without the list: is 57 prime? What about 59? Hint: add up the digits of 57.

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