I'm performing hypergeometric test in R on following data:

• set1 of genes - 1383
• set2 of genes - 3510
• overlap - 686
• total gene number in population - 25059

using following code phyper(685,1383,25059-1383,3510,lower.tail = F,log.p = FALSE) the output is:

[1] 1.492322e-236

However, if I use the same sets of genes but my overlap is now bigger: 886 genes, the pvalue returned by function is 0: phyper(885,1383,25059-1383,3510,lower.tail = F,log.p = FALSE)

[1] 0

Why the p-value is growing? Shouldn't my overlap be more significant in the second case? What is the logic behind these results?

Thanks a lot!