The RSA numbers are semiprimes (numbers that are the product of two prime numbers) that were given in the non-discontinued RSA Factoring Challenge. It is believed that factoring large numbers (assuming the factors are similar in magnitude) without a quantum computer is extremely difficult, which would be indispensable in cryptography due to its tremendous parallel processing capabilities. The RSA numbers range from 100 to 617 digits (2048 bits) in size. RSA Security has established cash prizes for factorizations of some of the numbers.
As of 2013, the largest successfully factored is RSA-768, which has 232 digits (768 bits, hence its name). It's full decimal expansion is
12301866845301177551304949583849627207728535695953347921973224521517264005072 63657518745202199786469389956474942774063845925192557326303453731548268507917 026122142913461670429214311602221240479274737794080665351419597459856902143413
(the line breaks are only included to fit the expansion fully visible) and its two prime factors are
3347807169895689878604416984821269081770479498371376856891 2431388982883793878002287614711652531743087737814467999489, 3674604366679959042824463379962795263227915816434308764267 6032283815739666511279233373417143396810270092798736308917
both of which have 116 digits, just over a googol.