Googol

In 1938, the famous American mathematician Edward Kazner walked around the park with his two nephews and discussed large numbers with them. During the conversation, we were talking about a number with one hundred zeros, which did not have its own name. One of the nephews, nine-year-old Milton Sirotta, suggested calling this number “googol” ( English googol ). A name was also proposed for another number: " googolplex ", numerically equal to ten in the googol degree. In 1940, Edward Casner, together with James Newman, wrote the popular science book “ New Names in Mathematics ”, where he told mathematics lovers about the numbers of googles and googolplex. ^[one]

Like all degrees 10, googol has only two simple divisors - 2 and 5. The total number of integer divisors of the number of googles exceeds 10 thousand. ^[2]

The binary representation of a googol consists of 333 bits , of which the last 100 digits are zeros:

0001 0010 0100 1001 1010 1101 0010 0101 1001 0100 1100 0011 0111 1100 1110 1011 0000 1011 0010 0111 1000 0100 1100 0100 1100 1110 0000 1011 1111 0011 1000 1010 1100 1110 0100 0000 1000 1110 0010 0001 0001 1010 0111 1100 1010 1010 1011 0010 0100 0011 0000 1000 1010 1000 0010 1110 1000 1111 0001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 ₂

A record in the hexadecimal system of a googol consists of 84 characters, of which the last 25 digits are zeros:

1249 AD25 94C3 7CEB 0B27 84C4 CE0B F38A CE40 8E21 1A7C AAB2 4308 A82E 8F10 0000 0000 0000 0000 0000 0000 ₁₆

Googol can be roughly estimated from above as factorial 70, which exceeds googol by about 20%:

70! = 11 978 571 669 969 891 796 072 783 721 689 098 736 458 938 142 546 425 857 555 362 864 628 009 582 789 845 319 680 000 000 000 000 000 ≈ 1.197857 × 10 ¹⁰⁰

Using the system of naming large numbers officially adopted in Russia , the USA and in a number of other countries, a googol can be called ten duotrigintillions , the etymology of which is associated with the Latin numeral 32 and means that it is necessary (32 + 1) to take 3 zeros - the ending is "illion" . If you use a long scale , then googol can be called ten cedeilliards .

The term “googol” has no serious theoretical and practical meaning. Kazner proposed it in order to illustrate the difference between an unimaginably large number and infinity , and for this purpose the term is sometimes used in teaching mathematics .

Googol is larger than the number of atoms in the known part of the Universe, of which, according to various estimates, there are from 10 ⁷⁹ to 10 ^{81 [3]} , which also limits its use.

The name of Google is a distorted spelling of the word "googol" ( English googol ) ^[4] . The creators of the famous search engine wanted to use the term “googol” as a name, but upon registration it turned out that such a domain was already taken. Many Internet services of Google have records in the reverse DNS zone ending with the suffix “1e100.net”, which is an option for writing the number of “googles” in exponential notation (a unit multiplied by 10 to a power of 100).

The word googol was the answer to the £ 1 million prize question on September 10, 2001 in the British television game Who Wants to Be a Millionaire? ". The answer was given correctly, but the participant was later convicted of fraud ^[5] .