# 1259 Graveyard Marker

This is the first of a week’s worth of Halloween Find the Factors puzzles. Graveyards are often associated with the holiday. Many graveyards have crosses marking the place where some dearly loved person was laid to rest. This puzzle isn’t very scary. Have fun solving it! Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Now I’ll share some facts about the number 1259:

• 1259 is a prime number.
• Prime factorization: 1259 is prime.
• The exponent of prime number 1259 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1259 has exactly 2 factors.
• Factors of 1259: 1, 1259
• Factor pairs: 1259 = 1 × 1259
• 1259 has no square factors that allow its square root to be simplified. √1259 ≈ 35.48239

How do we know that 1259 is a prime number? If 1259 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1259 ≈ 35.5. Since 1259 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1259 is a prime number. 1259 is the sum of the twenty-five prime numbers from 5 to 103.

The number after 1259 has thirty-six factors. No wonder 1259 had to settle for 1 and itself being its only factors.

Between prime numbers 1237 and 1277, there are 39 numbers but only two of them are prime numbers. 1259 is one of them. Up to 1277 on the number line, no other segment of the same length has a lower incidence of prime numbers than that!