Is memorizing the Quran with the intention of worldly competition considered hypocrisy or insincere intention?

You have done well by agreeing with your friend to compete in memorizing the Qur’an, for this is a form of cooperation in righteousness and piety. Disregard the whispers of Satan that delude you into thinking your work is for other than Allah, and continue on your path, sincere to Allah Almighty, and mindful of the nobility of memorizing the Qur’an. Strive for sincerity and cast away evil thoughts.