It's a really big number equivalent to:
2^43,112,609 - 1
That's 2 to the 43 million 112 thousand 609 power, then subtract 1.
316,470,269,330,255,923, ..., 022,181,166,697,152,511
That prime number has 12,978,189 digits, so don't ask me to write them all here for you, but if you are interested, I've given you a link.
It was discovered August 23, 2008 on a UCLA computer running "Primenet" software as part of the "Greater Internet Mersenne Prime Search" (GIMPS) project. It is listed as the 45th Mersenne Prime (of the form 2^p - 1).
Two weeks later (September 6, 2008) another Mersenne prime number was discovered in Cologne, Germany but it has slightly fewer digits than the first (This prime is listed as the 46th Mersenne Prime in discovery order, but the record for largest discovered to date is the 45th Mersenne prime.)
In English, the largest prime number starts,
"Three hundred sixteen quattuormilliamillia trecensexviginmillia unsexagintillion,
four hundred seventy quattuormilliamillia trecensexviginmillia sexagintillion,
two hundred sixty nine quattuormilliamillia trecensexviginmillia novemquinquagintillion,
three hundred thirty quattuormilliamillia trecensexviginmillia octoquinquagintillion, ..."