If this hypothesis is correct, that would mean that when you’re sieving up to 1 trillion, you can cross off multiples of 2, then 3, then 5, and keep going until the inclusion/exclusion sum starts to involve divisors over about 1 million — beyond that point, you can’t calculate the terms in your sum. In… Continue reading A New Generation of Mathematicians Pushes Prime Number Barriers
Tag: Quantum Stuff
A Brief History of Tricky Mathematical Tiling
Quanta Magazine > 0; if (typeof predicate !== ‘function’) { throw new TypeError(‘predicate must be a function’); } var thisArg = arguments[1]; var k = 0; while (k We care about your data, and we’d like to use cookies to give you a smooth browsing experience. Please agree and read more about our privacy policy.Agree… Continue reading A Brief History of Tricky Mathematical Tiling
Bats Use the Same Brain Cells to Map Physical and Social Worlds
A fruit bat hanging in the corner of a cave stirs; it is ready to move. It scans the space to look for a free perch and then takes flight, adjusting its membranous wings to angle an approach to a spot next to one of its fuzzy fellows. As it does so, neurological data lifted… Continue reading Bats Use the Same Brain Cells to Map Physical and Social Worlds
The Hidden Connection That Changed Number Theory
There are three kinds of prime numbers. The first is a solitary outlier: 2, the only even prime. After that, half the primes leave a remainder of 1 when divided by 4. The other half leave a remainder of 3. (5 and 13 fall in the first camp, 7 and 11 in the second.) There… Continue reading The Hidden Connection That Changed Number Theory
Here’s Why Salt Water Is Invading the Mississippi and Whether It Will Happen More Often
CLIMATEWIRE | The drought-driven wedge of salt water creeping up the Mississippi River is deepening a mystery about one of the world’s mightiest waterways. How will climate change affect the river? There are relatively few scientific studies on how warming is reshaping the Mississippi, and even fewer on saltwater intrusion from the Gulf of Mexico. The… Continue reading Here’s Why Salt Water Is Invading the Mississippi and Whether It Will Happen More Often
How to Watch the Northern Lights and Other Awesome Auroras
Imagine standing under the starry vault, bundled against the cold, when the sky erupts overhead. Rippling curtains, ribbons and streamers of colors across the rainbow light up the night, shimmering and majestic and all eerily silent. That’s what it’s like to see a vivid auroral display, and being able to witness one for yourself is… Continue reading How to Watch the Northern Lights and Other Awesome Auroras
The AI Boom Could Use a Shocking Amount of Electricity
Every online interaction relies on a scaffolding of information stored in remote servers—and those machines, stacked together in data centers worldwide, require a lot of energy. Around the globe, data centers currently account for about 1 to 1.5 percent of global electricity use, according to the International Energy Agency. And the world’s still-exploding boom in… Continue reading The AI Boom Could Use a Shocking Amount of Electricity
Icy Oceans Exist on Far-Off Moons. Why Aren’t They Frozen Solid?
They’d based their prediction on the orbital dance of Jupiter’s largest moons. For every four orbits that Io completes, Europa makes two and Ganymede one. This orbital configuration, known as a resonance, causes Io to wobble back and forth, making its orbit elliptical. When Io is closer to Jupiter, the planet’s gravity yanks on it… Continue reading Icy Oceans Exist on Far-Off Moons. Why Aren’t They Frozen Solid?
The Mathematician Who Shaped String Theory
Eugenio Calabi was known to his colleagues as an inventive mathematician — “transformatively original,” as his former student Xiuxiong Chen put it. In 1953, Calabi began to contemplate a class of shapes that nobody had ever envisioned before. Other mathematicians thought their existence was impossible. But a couple of decades later, these same shapes became… Continue reading The Mathematician Who Shaped String Theory
Thirty Years Later, a Speed Boost for Quantum Factoring
Finding Factors Quantum computers derive their power from the peculiar way they process information. Classical computers use bits, each of which must always be in one of two states, labeled 0 and 1. Quantum bits, or “qubits,” can additionally be in combinations of their 0 and 1 states — a phenomenon called superposition. It’s also… Continue reading Thirty Years Later, a Speed Boost for Quantum Factoring