# 1723 A Little Virgács

Contents

### Today’s Puzzle:

I haven’t blogged much this year so I guess I deserved a little bit of virgács in my shoes this morning. Mikulás (St. Nick) leaves virgács in the boots of naughty little boys or girls in the wee hours of December 6. Treats are for the good kids. What is virgács? It is small golden spray-painted twigs bound with some pretty red ribbon.  Of course, all children are sometimes naughty and sometimes nice, so they could all expect to get virgács along with their treats in their boots this morning.

You can solve this virgács puzzle by starting with the clues at the top of the grid, finding their factors, and working down the puzzle row by row until you have found all the factors. Each number from 1 to 10 must appear exactly one time in both the first column and the top row.

### Factors of 1723:

• 1723 is a prime number.
• Prime factorization: 1723 is prime.
• 1723 has no exponents greater than 1 in its prime factorization, so √1723 cannot be simplified.
• The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1723 has exactly 2 factors.
• The factors of 1723 are outlined with their factor pair partners in the graphic below.

How do we know that 1723 is a prime number? If 1723 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1723. Since 1723 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, or 41, we know that 1723 is a prime number.

### More About the Number 1723:

1723 and 1721 are twin primes.

1723 is the sum of consecutive numbers:
861 + 862 = 1723.

1723 is the difference of consecutive squares:
862² – 861² = 1723.

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