Answering the challenge

It is possible to easily decode RSA messages if you know the two prime factors p and q. The strength of the system is based on the conjecture that it is extremely hard to factor large integers. In 1977, the year of the challenge, Rivest made some estimates on time of computation based on 1977 technology. It took less than 7 minutes on a PDP-10 to test the primality of 130-digit numbers. To find the first prime number after 2²⁰⁰ took under 45 seconds. He estimated the time necessary to factor a 126-digit number equal to the product of two 63-digit primes at 40 quadrillion years (that is, $40\times 10^{15}$, or 4 million estimated lifetimes of the universe). The estimate proved a shade conservative.

On April 27, 1994, the factorization n=pq with
$$\begin{align*}p=\ & 34905295108476509491478496199038 \\ & 98133417764638493387... ...1329932667095499619881908344\\ & 61413177642967992942539798288533 \end{align*}$$
was announced, after less than eight months of computation by a worldwide network of computers. It was determined that
$$\begin{align*}d=\ & 106698614368578024442868771328920 \\ & 1547807099066339378... ...631259117744708733401685974 \\ & 62306553968544513277109053606095 \end{align*}$$
The plaintext to the challenge may then be computed as
$$\begin{align*}P\equiv C^d \equiv\ & 20080500130107090300231518041900 \\ & 01180500191721050113091908001519 \\ & 19090618010705 \end{align*}$$
which translates as

20	08	05	00	13	01	07	09	03	00	23	15	18	04	19
T	H	E		M	A	G	I	C		W	O	R	D	S
00	01	18	05	00	19	17	21	05	01	13	09	19	08	00
	A	R	E		S	Q	U	E	A	M	I	S	H
15	19	19	09	06	18	01	07	05
O	S	S	I	F	R	A	G	E

The factorization was the result of eight months of computation by a network of hundreds of computers worldwide. On behalf of all those involved, the one hundred dollar reward was duly collected and donated to the GNU project of the Free Software Foundation.