Summation of Primes
The sum of the primes below $10$ is $2 + 3 + 5 + 7 = 17$. Find the sum of all the primes below two million....
-
John Rhodes
-
August 15, 2023
Special Pythagorean Triplet
A Pythagorean triplet is a set of three natural numbers, $a \lt b \lt c$, for which, $$a^2 + b^2 = c^2.$$ For example, $3^2 + 4^2...
-
John Rhodes
-
August 15, 2023
Largest Product in a Series
The four adjacent digits in the $1000$-digit number that have the greatest product are $9 \times 9 \times 8 \times 9 = 5832$. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557...
-
John Rhodes
-
August 15, 2023
$10001$st Prime
By listing the first six prime numbers: $2, 3, 5, 7, 11$, and $13$, we can see that the $6$th prime is $13$. What is the $10\,001$st...
-
John Rhodes
-
August 15, 2023
Sum Square Difference
The sum of the squares of the first ten natural numbers is, $$1^2 + 2^2 + … + 10^2 = 385.$$ The square of the sum of...
-
John Rhodes
-
August 15, 2023
Smallest Multiple
$2520$ is the smallest number that can be divided by each of the numbers from $1$ to $10$ without any remainder. What is the smallest positive number...
-
John Rhodes
-
August 15, 2023
Largest Palindrome Product
A palindromic number reads the same both ways. The largest palindrome made from the product of two $2$-digit numbers is $9009 = 91 \times 99$. Find the...
-
John Rhodes
-
August 15, 2023
Largest Prime Factor
The prime factors of $13195$ are $5, 7, 13$ and $29$. What is the largest prime factor of the number $600851475143$? We can find the largest prime...