Prime Sum!

Number Theory Level 4

Find the sum of all the prime numbers less than 1000 that come just after a perfect square.

For example, 2 is a prime that comes just after a perfect square 1.


The answer is 2271.

Adithya Rajeev by Adithya Rajeev , 23, India

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1 solution

Uahbid Dey
Sep 6, 2015
  1. Since all odd number squares makes a odd number, hence the next number will be even and hence it will not be a prime number (Exception 1²+1= 2). .
  2. 32² >1000, hence, the root number must be <32. .
  3. If last digit is 2 or 8, e.g. 8, 12, 18, 22, 28 next number after squaring would give a number having last digit as 5, hence not prime number (Exception: 2² + 1= 5). .
  4. So, remains, 1, 2, 4, 6, 10, 14, 16, 20, 24, 26, 30. whose (square +1) gives 2, 5, 17, 37, 101, 197, 257, 401, 577, 677, and 901(17x53). .
  5. So, sum = 2 + 5 + 17 + 37 + 101 + 197 + 257 + 401 + 577 + 677 = 2271
1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice way to eliminate so many possibilities.

Calvin Lin Staff - 5 years, 9 months ago

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