There are no specific prayers other than confessing you are a sinner and asking Jesus into your heart, Romans 10:9-10, Rev 3:20. There is nothing wrong with what they call "The Sinners Prayer" if you humble yourself before the Lord in all sincerity. Unfortunately so many just repeat the words and think they are saved like I did so many years ago as I thought just repeating that prayer was all I had to do to keep me from going to hell.You are correct. And you can prove me disqualified right now. If you and the others are correct and “calling on the name of the Lord” for salvation under the new covenant means prayer; then show me ONE just ONE example in the NT of an alien sinner needing salvation praying for it and you can prove me to be disqualified. But, if you don’t provide this then what does that say about you?
John 3:3 Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God.
How does one become born again?
Rom 10:9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
Rom 10:10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.