How Far Away Is 1344 from the Nearest Prime Number?

1344 is 17 numbers away from the nearest prime number. 17-away is a new record for distance to the closest prime number!

1344 will hold that record until prime number 2179 claims it with being 18-away from the nearest prime:
2161–(18 composite numbers)–2179–(24 composite numbers)–2203

Stetson.edu mentioned the previous two numbers, 1342 and 1343, breaking the 15-away and the 16 away records respectively, but didn’t mention this one. I guess it considered 1344 being the order of a perfect group to be more important.

Here’s more about the number 1342:

  • 1344 is a composite number.
  • Prime factorization: 1344 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7, which can be written 1344 = 2⁶ × 3 × 7
  • 1344 has at least one exponent greater than 1 in its prime factorization so √1344 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1344 = (√64)(√21) = 8√21
  • The exponents in the prime factorization are 6, 1 and 1. Adding one to each exponent and multiplying we get (6 + 1)(1 + 1)(1 + 1) = 7 × 2 × 2 = 28. Therefore 1344 has exactly 28 factors.
  • The factors of 1344 are outlined with their factor pairs in the graphic below.

 

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