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Ask Ars: Why spend time and money finding new prime numbers?

Are we wasting computer power looking for new numbers with certain properties?

In 1998, Ask Ars was an early feature of the newly launched Ars Technica. Now, as then, it's all about your questions and our community's answers. We occasionally dig into our question bag, provide our own take, then tap the wisdom of our readers. To submit your own question, see our helpful tips page.

OK, you've got us. The jig is up. There is no use for absurdly large prime numbers—yet (we’ll explain that eventually). Slightly less ludicrous prime numbers do have a point, which we'll describe here.

One modern day instance of practical use for prime numbers is in RSA encryption, which allows two parties to pass secret messages back and forth using independent encryption and decryption codes. In RSA, someone who wants to receive a private message will publish a product of two large prime numbers as their "public key," which senders can use to encrypt messages intended for the key publisher.

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Pigeons match primates in number sense

By now, we all know that being called a "birdbrain" isn’t really an insult; birds have been shown to have several higher-order cognitive skills that we previously thought only primates had the brains for. Jays are capable of episodic memory, parrots can solve multi-step puzzles and use a succession of tools to get a food item, and crows have even learned to use city traffic and stoplights to their advantage. Now, Science reports yet another cognitive area where birds are on par with primates: they have a sense of numbers.

In 1998, a pair of researchers used a novel experiment to show that rhesus monkeys had numerical competence; in other words, they could use abstract numerical rules. The monkeys were shown a set of three images picturing one, two, and three items, and were trained to choose these images in ascending order. Once they had been trained to a certain accuracy level, they were shown numbers of items that they hadn’t necessarily seen before. The monkeys were generally able to choose the greater of the two numbers, even when they didn’t have experience with the values involved. Clearly, they had learned not only the values they were trained on, but also more abstract rules about numerosity.

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