Does praying for all people reach a specific person whom I do not know, or is its reach limited to whoever was on my mind at the time of the prayer?

Supplicating for the well-being of all Muslim men and women in this world and the Hereafter is prescribed, and it is a manifestation of brotherhood, for a Muslim loves for his brother what he loves for himself. If a Muslim generally supplicates for his brethren, it is hoped that all of them will be touched by its blessings. The Prophet (peace and blessings be upon him) said in the Tashahhud: "Peace be upon us and upon the righteous servants of Allah, for if you say it, it will reach every righteous servant of Allah in the heavens and on earth." And if one intends to supplicate for a specific person and also supplicates for all Muslims, it is hoped that his supplication will reach them; as mentioned in the funeral prayer: "O Allah, forgive our living and our dead, our young and our old, our males and our females, those present and those absent." Scholars have explained that the purpose of these phrases is to encompass and include all Muslim men and women.