A Baltimore rabbi once joked that he almost became a disbeliever from driving throughOregon. Torah tells us that everything that Hashem created has a purpose even every single leaf on every tree. The rabbi said that for hundreds of miles along the Interstate he passed an uncountable number of trees — how could each leaf have a purpose in the great scheme of the world?

The same thing could be said about many curiosities with which mathematicians amused themselves for ages.

Mathematicians have always been fascinated by numbers. Of course numbers are important for we could not manage our lives without them but mathematicians were generally not concerned with usefulness; they studied numbers purely for their own sake. One of the most fascinating albeit seemingly useless studies was that of “prime numbers.”

The number 6 is equal to 2 multiplied by 3. Because it can be written as the product of two numbers it is called a composite number. Similarly 12 which is the product of 2 x 2 x 3 is also a composite number. The numbers 5 or 11 however cannot be divided into products of other numbers. They are called prime numbers.

How large can a number be and still be prime? Over two thousand years ago mathematicians proved that there are an infinite number of primes. There is none that is the largest.

Although much is now known about primes there are still mysteries. For example both 11 and 13 are prime and they differ by two which is the closest that two prime numbers can be to each other. This is also true of 59 and 61. Such pairs of numbers are known as twin primes. How many twin prime pairs exist? Many mathematicians guess that there are an infinite number of them but so far no one has been able to prove this “twin prime conjecture.”

Another amazing pattern is found in all even numbers greater than 4. The number 10 can be written as the sum to two primes 3 and 7. This is also true of the number 100 which is equal to 17 plus 83. In 1742 a mathematician named Christian Goldbach speculated that this is true for all even numbers no matter how large. To date no one has been able to prove “Goldbach’s conjecture” and it remains an area of active mathematical research.

No one has been able to develop a theory of why certain numbers are prime and why others are not. Indeed given a large number it is still a hard task involving high speed computers to determine if it is prime and if not it is quite a formidable task to determine what all its factors are.

Huge sums of money are being spent on prime number research today. But — why is this? Isn’t prime number research just a curiosity for nerdy mathematicians? Not any longer. In 1978 three men named Ronald Rivest Adi Shamir and Leonard Adelman published a paper in which they described a radically new way of encrypting messages.

The eponymous RSA algorithm became the leading example of the field of “public key cryptography.” The amazing new property of this technique is that a person can publicly reveal a code based on an enormous composite number. Anyone can then take a message encrypt it and send it to the originator of the number. But no one but the originator can decipher it unless they can factor the publicly revealed number into its primes which for huge numbers is a task that is so difficult that it is still beyond the capability of even the most powerful computers.

Each time a person logs into their online bank account or pays for something with a credit card they are sending messages that are encrypted using the RSA algorithm on the assumption that no unauthorized person will be able to factor the associated huge numbers to read them. Prime number theory has become vital to the functioning of the world today. Even Ma’asu HaBonim Haysa leRosh Pinah — the stone discarded by the builders has become the corner stone. Everything in Hashem’s universe is indeed vitally important: every number every leaf and certainly every person.