Is there a way to find these Prime Numbers??


As we discussed in the "The Search" tab of this website, we are constantly searching for these new prime numbers but it is a grueling and labor intensive process. Even "GIMPS ", which is an international effort consisting of hundreds of thousands of computers, has only discovered 14 new primes since its creation in 1996 (www.mersenne.org). We have ways us testing for primality, but thus far we have no real way of generating new prime numbers.

This leaves us with the question that has taunted mathematicians for centuries. Is there a way? Is there a method yet to be discovered that will allow us to generate prime numbers? Is there a pattern to the apparent randomness of prime numbers that we can harness in order to find more of them?

The following is the story of a pair of incredibly gifted twins that may have held the key to finding/generating these large prime numbers. This story comes from a famous essay by Oliver Sacks called "The Man Who Mistook His Wife for a Hat and Other Clinical Tales"(1985), the italicized portions are direct quotes from the essay.

The Twins

John and Michael

In this splendid essay written my Oliver Sacks He talks of his encounter with two twins named John and Michael. These two twins were autistic and had an estimated IQ of only 60, but they were labeled " idiot savants " due to their remarkable memory and calculative abilities. They had already been on TV various times performing their " calendar trick ".

"The twins say, ‘Give us a date, any time in the last or next forty thousand years.’ You give them a date, and, almost instantly, they tell you what day of the week it would be. ‘Another date!’ they cry, and the performance is repeated."

But Upon meeting John and Michael, Oliver Sacks realized that there was much more to their genius than a simple calendrical algorithm. For example Mr. Sacks was astounded when he witnessed the following.

"A box of matches on their table fell, and discharged its contents on the floor: ‘111,’ they both cried simultaneously; and then, in a murmur, John said ‘37’. Michael repeated this, John said it a third time and stopped. I counted the matches, it took me some time, and there were 111.
‘How could you count the matches so quickly?’ I asked. ‘We didnt count,’ they said. ‘We saw the 111.’ "


The scene shown below from the popular movie "Rain Man" (1988) was actually inspired by the twins John and Michael (Milwaukee Journal, Dec. 18 1988).





But more interesting than their abilities to predict dates, or visualize quantities was discovered as they played a simple game together.

" They were seated in a corner together, with a mysterious, secret smile on their faces, a smile I had never seen before, enjoying the strange pleasure and peace they now seemed to have. I crept up quietly, so as not to disturb them. They seemed to be locked in a singular, purely numerical, converse. John would say a number, six-figure number. Michael would catch the number, nod, smile and seem to savor it. Then he, in turn, would say another six figure number, and now it was John who received, and appreciated it richly. They looked, at first, like two connoisseurs wine-tasting, sharing rare tastes, rare appreciations. I sat still, unseen by them, mesmerized, bewildered.
What were they doing? What on earth was going on? ... As soon as I got home I pulled out tables of powers, factors, logarithms and primes, mementos and relics of an odd, isolated period in my own childhood, when I too was something of a number brooder, a number see-er, and had a peculiar passion for numbers. I already had a hunch and now I confirmed it. All the numbers, the six-figure numbers, which the twins had exchanged were primes.
I returned to the ward the next day, carrying the precious book of primes with me. I again found them closeted in their numerical communion, but this time, without saying anything, I quietly joined them. They were taken aback at first, but when I made no interruption, they resumed their ‘game’ of six-figure primes. After a few minutes I decided to join in, and ventured a number, an eight-figure prime. They both turned towards me, then suddenly became still, with a look of intense concentration and perhaps wonder on their faces. There was a long pause,the longest I had ever known them to make, it must have lasted a half-minute or more, and then suddenly, simultaneously, they both broke into smiles.
They had, after some unimaginable internal process of testing, suddenly seen my own eight-digit number as a prime, and this was manifestly a great joy, a double joy, to them; first because I had introduced a delightful new plaything, a prime of an order they had never previously encountered; and, secondly, because it was evident that I had seen what they were doing, that I liked it, that I admired it, and that I could join in myself.
They drew apart slightly, making room for me, a new number playmate, a third in their world. Then John, who always took the lead, thought for a very long time, it must have been at least five minutes, though I dared not move, and scarcely breathed, and brought out a nine-figure number; and after a similar time his twin, Michael, responded with a similar one. And then I, in my turn, after a surreptitious look in my book, added my own rather dishonest contribution, a ten-figure prime I found in my book.
There was again, and for even longer, a wondering, still silence; and then John, after a prodigious internal contemplation, brought out a twelve-figure number. I had no way of checking this, and could not respond, because my own book, which, as far as I knew, was unique of its kind, did not go beyond ten-figure primes. But Michael was up to it, though it took him five minutes, and an hour later the twins were swapping twenty-figure primes, at least I assume this was so, for I had no way of checking it. Nor was there any easy way, in 1966, unless one had the use of a sophisticated computer. And even then, it would have been difficult, for whether one uses Eratosthenes sieve, or any other algorithm, there is no simple method of calculating primes. There is no simple method, for primes of this order, and yet the twins were doing it."



John and Michael

We may never know exactly how the twins were generating these incredibly large prime numbers, but the fact that they were able to produce them leaves us with the hope that there might actually be a way!




Go to top

I am AWESOME!!!