First Factoring of a 100-Digit Number
The first successful factoring of a 100-digit number occurred on October 11, 1988, marking a significant milestone in the field of mathematics. Factoring involves breaking down a large number into its smaller components, or factors, that divide it evenly without leaving a remainder. While simple with smaller numbers, this process becomes increasingly complex with larger ones, leading to practical applications in areas such as cryptography and code-breaking. The breakthrough was achieved through a collaborative effort among scientists and mathematicians from the University of Chicago and the Digital Equipment Corporation, utilizing a network of hundreds of computers across the United States and Europe. The specific number factored was 11 raised to the 104th power, plus 1. This accomplishment not only highlighted advancements in computational power but also underscored the importance of factoring in modern cryptographic systems, which rely on complex numerical calculations for security. The implications of these findings continue to resonate within both mathematical theory and practical applications today.
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First Factoring of a 100-Digit Number
First Factoring of a 100-Digit Number
On October 11, 1988, a 100-digit number was successfully factored for the first time. In mathematics, factoring is the process of determining how a large number may be divided by smaller numbers without leaving any remainder. For example, the number 20 has the factors 1, 2, 4, 5, 10, and 20 itself, because all those numbers divide cleanly into 20 without leaving any remainder. Nonfactors do not divide cleanly, and so, for example, the number 3 is not a factor of 20 because it divides into 20 six times (3 goes into 20 six times, and 6 times 3 equals 18) but leaves a remainder of 2 (20 minus 18 equals 2). Factoring a number—determining all of its factors, such as for the number 20 above—can be enormously difficult for large numbers but has practical applications beyond the realm of pure mathematics in the field of code-breaking. Modern cryptography is now generally based on extremely complex numerical calculations, and factoring can help break these codes down or help design more secure ones.
Using hundreds of computers networked from the United States, Western Europe, and other places around the world, scientists and mathematicians led by teams from the University of Chicago and the Digital Equipment Corporation were able to factor a 100-digit number for the first time. The number they factored was 11 raised to the 104th power, plus 1.