Indeed, there are meanings associated with certain numbers. At the same time, seeing significance in all numbers or in some numbers at all times is an extreme and could lead to gross error. With that note of caution, below is a brief review of a few numbers and their biblical significances.
The number one denotes unity or commencement. Paul wrote, "There is one body and one Spirit, . . . one Lord, one faith, one baptism" (Ephesians 4:4-5). Jesus Christ is the "firstborn from the dead" (Revelation 1:5).
The number three denotes completeness. Jesus rose the third day, Daniel prayed three times a day, Peter denied Christ three times, and Jesus Christ prayed three times to the Father before He was taken to be crucified.
The number seven denotes spiritual perfection. God created the seven-day weekly cycle and the
The number twelve also has a unique significance; it means organizational beginnings or governmental perfection. The twelve tribes of Israel conducted a physical type of God's government on this earth. Christ chose twelve apostles as the governmental foundation for His church.
The number forty suggests a time of testing and trial. Christ was tempted forty days by the Devil. Israel wandered in the wilderness forty years. Several Israelite kings reigned for forty years, while Moses' life breaks down into three forty-year periods.
Several other numbers may have spiritual significance, for instance, five (grace), six (man), eleven (disorder), thirteen (rebellion), etc. For additional information on biblical numbers, you may wish to consult Appendix 10 of The Companion Bible, in which E.W. Bullinger compiles his reasons for assigning meaning to several numbers. He also wrote a book on the subject, Number in Scripture: Its Supernatural Design and Spiritual Significance.