Anamika and Arsha are best friends, but there is no similarity between their behaviors except a single part of their character. They love to eat like crazy. Once these two friends went to Las Vegas to take part in a competition called $"World$ $Pasta$ $Eating$ $Championship"$. The person able to eat the most within a specific time would become the winner. Anamika and Arsha won the first position jointly, defeating all 400 participants in the competition, but the committee couldn't find out who was the better one between the two of them. As a result, they decided to arrange several individual competitions between these two friends to determine the winner, but all their attempts failed miserably. Seeing no the other choice, the committee decided to give them a mathematical problem. The first person to solve the problem would be declared the winner. The problem was as follows:
"Anamika and Arsha both took x bowls of pasta, where x is a prime number. x is also the biggest prime factor of the following number $34^{122}+34^{123}+34^{124}$".
How many bowls of pasta did they take?