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thanks for the answer about prayer of unbeleivers.We need to realise that God is all knowing,nothing takes Him by surprise,and is always working in the hearts of men,and I believe that when a person is calling out to God for help in any given situation before salvation,and the prayer is answered will lead to a recognition in the persons heart that he/she does have significance, and that may be the beginning of a dynamic new life in Christ!!
We should never underestimate the fact that God is not willing that anybody perish,and that His love and grce is so much wider,and deeper than any of us can even begin to imagine!!
Before I was a Christian 24 years ago I was in deep despair to the point of suicide. I layed on my bed and cried out "God if your real please show me".Well in the next 30 days boy did He show me which lead to several events I'd call miraculous and lead to me coming to accept Jesus as my Lord and Saviour. So I know He answers cries that are sincere for salvation.
I believe that God listens to all prayers from everyone & anyone that wants to call out to him. Why would he not listen to a sinner? God wants sinners to come to him, no matter what, so that they can be saved by his goodness. If a sinner says he that he does not believe & yet talks to God, then there is something in his heart that says he believes & that is the seed that God has planted & this sinner does truly believe that there is hope. Why take that away from him. Sinners repent all the time, if God didn't listen, then there would be no hope of change. God bless the sinners. Work in their hearts, listen to their cries for most do want to change & not be sinners anymore. God is their only hope, their only chance at this. I love when I hear stories of sinners & unbelievers hearts, minds & souls begin the journey of change & love.