Solution: Let the number of peaches taken by the fifth person be X, then there are * * * peaches: (5X+ 1).

Then the number of peaches taken by the fourth person is: (5X+ 1), and the number of peaches is: 5*(5X+ 1)+ 1.

=(25X+6) pieces

Then the number of peaches taken by the third person is: (25X+6), and the number of peaches * * * is: 5*(25X+6)+ 1.

=( 125X+3 1)

Then the number of peaches taken by the second person is (125X+3 1), and the number of peaches is: 5 * (125x+31)+1.

=(625X+ 156)

Then the number of peaches taken by the first person is (625X+ 156), and the number of peaches * * * is: 5*(625X+ 156)+ 1.

=(3 125X+78 1)

When X= 1, the number of peaches is the least.

So the number of peaches is at least: 3 125X+78 1.

=3 125* 1+78 1

=3906