My youngest grandchild is 7 months old and is just beginning to crawl. He stops crawling periodically to wipe drool off his own face. It’s pretty funny.
Here’s today’s puzzle:
Print the puzzles or type the solution on this excel file: 10-factors 807-814
- 811 is a prime number.
- Prime factorization: 811 is prime.
- The exponent of prime number 811 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 811 has exactly 2 factors.
- Factors of 811: 1, 811
- Factor pairs: 811 = 1 x 811
- 811 has no square factors that allow its square root to be simplified. √811 ≈ 28.4780617
How do we know that 811 is a prime number? If 811 were not a prime number, then it would be divisible by at least one prime number less than or equal to √811 ≈ 28.5. Since 811 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, or 23, we know that 811 is a prime number.
811 is the second half of a twin prime, and it is also the sum of five consecutive prime numbers:
- 151 + 157 + 163 + 167 + 173 = 811.
OEIS.org informs us that the smallest prime factor of 24!+1 is 811. Wow! Really?
- If you type 24!+1 into your computer calculator you get 620,448,401,733,239,439,360,001.
- If you divide that number by 811, you get 765,041,185,860,961,084,291.
- If you type that into Number Empire’s Prime Number Checker, you will see that it is prime.
- Thus 811 is the smaller of 24!+1’s two prime factors!
Such perseverance from Bodhi is inspiring! Still, thank you for not challenging us to find the five prime numbers that create 811,
Oh, but you were sometimes the very best at finding them! Now that I’ve saved you the time looking for them, you’ll have a little more time to make handmade books, fold paper and write about your creations. We love that you do that.