What is the biggest number known to mankind? Is it possible to write it down, and above all, does something like that even have the right to exist? Let’s find out what modern science says about it.
What is the biggest number in the world?
While we are able to find many examples of huge numbers in modern science, none of them is the greatest. After all, there is no objective limit to which we could try to count ourselves – numbers can be increased infinitely, for example by adding 1 to the next one that has been applied.
Googol – can it be awarded the title of the biggest number?
Googol is a number of 10 to the power of 100, traditionally taking the form of one hundred zeros preceded by one. The name was coined by nine-year-old Milton Sirott, the nephew of mathematician Edward Kasner. The researcher described the nephew’s creation and popularized the term in the scientific community. Knowing that the number of atoms in the observable universe is 10 to the power of 80, it is fairly easy to say that googol is a value that significantly exceeds this number. The success of the number contributed to the expansion of its multiples, such as googolplex which is equal to 10googol. Similarly, values such as googolplexian (10googolplex) and googolplexianth (10googolplexian) were created.
Graham’s number – is it greater than a googol? What is it basically?
As it turns out, even such huge values as googol multiples cannot match Graham’s number. Its name comes from the name of the mathematician who first described it. While working on proving the Ramsey theorem, Ronald Graham estimated the extreme values of the range that could include a number satisfying this theorem. The upper estimate of the Ramsey theorem solution is precisely the Graham number. It was considered to be the largest positive integer used in practice in a published mathematical proof, thanks to which it found its way to the pages of the Guinness Book of Records for the same reason.
It is most commonly known as G64. However, can it be written in the decimal system? Absolutely not. The reason for this is that it contains such a huge number of digits that if each digit were assigned one atom, their sum would significantly exceed the sum of the atoms in the universe. It is still unknown how many digits Graham’s number has. It must therefore be recorded using a special notation that is able to take into account such unimaginably large values. This type of notation is known as Knuth’s sagittal notation and relies on iterated (repeated) exponentiation.
Searching for the largest known prime number
Another criterion that we can adopt in determining the largest known number to mankind may be that the tested numbers have only two divisors. So what could the largest prime number be? Experts from around the world focused on this issue, developing a variety of software that checks huge numbers against this criterion. In December 2017, the current record holder was selected, i.e. the prime number 277,232,917-1. This was done by the American electronics engineer Jonathan Pace, who participated in the search for large primes called GIMPS.
It took the Intel I5-6600 CPU six days of uninterrupted operation to verify that this value was in fact prime. The process was additionally extended by the need to repeat the calculations on four other devices in order to confirm the accuracy of the result. How exactly did the counting process go? The computer multiplied 77222917 2 by itself, and then subtracted 1 from the result. The next step was just to check if the number really has only two divisors, and after dividing you do not get the remainder.
Can such huge numbers be applied to anything at all?
Although such great values do not have the potential for practical application, their existence may have a different purpose. The mathematician Edward Kasner, who described and spread the concept of googol, uses this number as a way of explaining the difference between a huge number and infinity. One of the other uses of this order is to represent all kinds of relationships between large numbers. Terms such as googol can therefore be used, for example, to name and easier imagine such great values.
Humanity does not have the technology with the operational power to process such values, let alone put them into practice. Thus, unimaginably large numbers remain a fascinating and somewhat scary thought experiment reminding us of the power of mathematics.
The biggest number in the world is a concept that without a doubt ignites the imagination. Some of the mysteries of the world of large numbers are still waiting to be solved, and although they are not the easiest ones, the most eminent minds in the world have to deal with them. Who knows what the future holds for huge numbers? Will it be possible to turn the unimaginable into the imaginable? We can only guess.