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Big numbers are everywhere, from the cells in the human body to the size of the universe. But once numbers edge past the realm of the physical, the human mind can struggle to grasp the sheer awesome scale of these numbers. Even infinity can seem easier to understand in comparison — it just goes on and on. And once numbers start to get large enough, everything starts to blur together, said Jon Borwein, an applied mathematician at the University of Newcastle in Australia.
"We don't understand numbers on this scale," Borwein said.
From the humble trillion to Graham's number, here are some of the most mind-boggling numbers there are.
Big is relativeSlide 2 of 19
Big is relative
When thinking about a personal budget, a $16 trillion debt ceiling is pretty inconceivable. But on the scale of the atoms in the universe, it looks absolutely paltry in comparison, said Scott Aaronson, a computer scientist at MIT.
To try to understand huge numbers, most people rely on analogies of scale. For instance, Carl Sagan famously likened the age of the universe to a calendar year, with humans only showing up in the last few hours of New Year's Eve.Slide 3 of 19
Riemann HypothesisSlide 4 of 19
First stated in 1859, the Riemann hypothesis is one of the greatest unsolved conjectures of mathematics, and whoever solves it will nab a $1 million prize. "This is the biggest open question in mathematics, the one that will guarantee your name is known in 10,000 years," Borwein said.
The hypothesis, if true, has important implications for the distribution of prime numbers, which aren't divisible by anything other than themselves or one. To test the hypothesis, mathematicians look for extremely large primes — those bigger than about 10 raised to the power of 30, he said. That may sound abstract, but it has many real-world implications, Borwein said. "Primes are embedded in everything we use for encryption," he said. "That all relies on stuff where the algorithms are designed using properties of primes that we think are true but don't know."Slide 5 of 19
The UniverseSlide 6 of 19
As far back as Archimedes, philosophers have wondered how many tiny particles could fit in the universe. Archimedes estimated that about 10 to the power of 63 grains of sand could fill the universe. He used a series of extremely rough estimates — the poppy seeds that make a grain of sand, the grains of sand that would cover the length of a stadium, and the stadia lengths between Earth and the sun, said Henry Mendell, a classical historian at California State University, Los Angeles.
Despite his crude measures, he wasn't too far off. Current estimates put the total number of atoms in the universe at about 10 to the 80.Slide 7 of 19
Quantum Fudge FactorSlide 8 of 19