383 is in only one Pythagorean triple, and it’s primitive

Although it would take awhile to count to 383, it is still a relatively small number. If you scroll down, you will see that it is also a prime number. Since all odd numbers greater than one are the short legs of a primitive Pythagorean triple, 383 is also. I will explain how to find that primitive triple using the Flintstones, the primitive yet modern stone age family as an analogy. You can use this method on ANY odd number greater than one to find a primitive triple:

• 383 is like Pebbles the shortest one in the family
• If we round down (383^2)/2 or 73344.5 to 73,344, we get a much bigger number, much like Fred is much taller than Pebbles in the family
• If we round the same expression up, we get 73,345, much like Wilma is just a little taller than Fred.
• 383 – 73344 – 73345 is a primitive Pythagorean triple just as Pebbles, Fred, and Wilma are a primitive yet modern stone age family of three. Test it out: (383^2) + (73344^2) = (73345^2)

Prime numbers can be one of the legs of only one Pythagorean triple, and it will always be a primitive. Sometimes prime numbers are the hypotenuse of a primitive Pythagorean triple, but 383 isn’t. In a future post, I’ll explain how to determine if a prime number is ever the hypotenuse.

Here is 383’s factoring information:

• 383 is a prime number.
• Prime factorization: 383 is prime.
• The exponent of prime number 383 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 383 has exactly 2 factors.
• Factors of 383: 1, 383
• Factor pairs: 383 = 1 x 383
• 383 has no square factors that allow its square root to be simplified. √383 ≈ 19.570

How do we know that 383 is a prime number? If 383 were not a prime number, then it would be divisible by at least one prime number less than or equal to √383 ≈ 19.570. Since 383 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 383 is a prime number.