Little Goldbach
Both 4 and 8 can be written as the sum of two prime numbers ($4=2+2$, $8=5+3$). How many numbers less than 20 cannot be written as the sum of two prime numbers?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
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A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
Thirty Six Exactly
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Strange Numbers
All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.