First Union Corp. said it expects to sign its millionth on-line customer next week.

The sixth-largest banking company said it will honor that customer with a slew of prizes including a personal computer, Internet access for two years, and a $5,000 credit on a First Union Check Card.

First Union will also award the same prizes to the bank employee who assists the millionth customer.

The bank said on Sept. 23 that it had about 964,000 on-line customers and was adding an average of 5,000 new ones each day. Most of them bank through the First Union Web site.

Last month Wells Fargo reported its millionth Internet customer and awarded him $10,000, a computer, and several other prizes.

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