Question

Take the following problem: “how many numbers are in a given range of integers, from which both their sum of digits and the sum of its square are prime?”

I was watching around codereview, and here I found an interesting question and tried to solve it.

So one can check prime numbers in a ordinary fashion, i.e. using a for loop from 2 to i and check for divisibility.

The interesting thing is here. BlueRaja - Danny Pflughoeft suggests a trick: “Since you only need to sieve to the square root of the number you’re testing for primality, you only need to run your sieve from 3 to*sqrt(⌈log10(B)⌉*81)“.

I have a question regarding implementation of Sieve of Eratosthenes.
what is the size of boolean array, which contains numbers to process for sieve.? can somebody write a code or any hint?

Answer 1

Here’s an example of the implementation of the Sieve of Eratosthenes using Java: link.

For the second part of your questions see this link:

“The maximum sum of squares-of-digits of an n-digit number is n*9*9 = n*81. The number of digits in a number B is ⌈log10(B)⌉. Since you only need to sieve to the square root of the number you’re testing for primality, you only need to run your sieve from 3 to sqrt(⌈log10(B)⌉*81). Even for B = 1 billion, this means the max you need to sieve to is 28.”