# 941 and Level 6

Today daylight savings time ends in the United States. That gives you an extra hour to sleep or do whatever you want. Perhaps you could spend part of your extra hour solving today’s puzzle: Print the puzzles or type the solution on this excel file: 10-factors-932-941

941 is a prime number that is also the sum of consecutive prime numbers two different ways:
179 + 181 + 191 + 193 + 197 = 941; that’s five consecutive primes
311 + 313 + 317 = 941; that’s three consecutive primes

29² + 10² = 941 That means 941 is the hypotenuse of a Pythagorean triple:
580-741-941 which can be calculated from 2(29)(10), 29² – 10², 29² + 10²

941 is also palindrome 575 in BASE 13 because 5(13²) + 7(13¹) + 5(13⁰) = 941

• 941 is a prime number.
• Prime factorization: 941 is prime.
• The exponent of prime number 941 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 941 has exactly 2 factors.
• Factors of 941: 1, 941
• Factor pairs: 941 = 1 × 941
• 941 has no square factors that allow its square root to be simplified. √941 ≈ 30.6757233

How do we know that 941 is a prime number? If 941 were not a prime number, then it would be divisible by at least one prime number less than or equal to √941 ≈ 30.7. Since 941 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, or 29, we know that 941 is a prime number. Here’s another way we know that 941 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 29² + 10² = 941 with 29 and 10 having no common prime factors, 941 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √941 ≈ 30.7. Since 941 is not divisible by 5, 13, 17, or 29, we know that 941 is a prime number.

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