Mole day is a time of celebration of the chemists most holy number: the mole. The mole is equal to 6.02 X 10^23. Therefore, mole day can be celebrated on June 2, at precisely 10:23 (am or pm) or October 23, at precisely 6:02 (am or pm).

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comment about proj's writeup:
That is very true, but Americans can also celebrate on 6/02 at 10:23 as well... (two mole days!)