Venting becomes less helpful, Cougle says, when it’s mean-spirited—when you’re just out to make your mother-in-law look bad, rather than make yourself feel better—or when you’re re-treading the same ground you’ve covered dozens of times before, keeping yourself stuck in that past anger without trying to move past it.

库格尔指出，当发泄变得刻薄无礼——即你只想让岳母出丑，而不是为了让自己感觉好一些——或者当你一再重复那些已经讨论过无数次的话题，让自己深陷于过往的愤怒而无法自拔，不愿向前看时，发泄就不再有益了。

What is the largest known prime number?

已知最大的素数是多少？

1

Prime numbers have been investigated for more than 2,000 years, since at least the era of the ancient Greek mathematician Euclid. There are infinitely many, but what is the largest known prime number?Prime numbers are those that can be evenly divided only by 1 and themselves, such as 3 and 7. They are key building blocks in math; per the fundamental theorem of arithmetic, every number greater than 1 is either a prime number or a multiple of a prime number, according to the University of Houston.

A major difference between real atoms and prime numbers is that the number of different types of stable atoms is finite. In contrast, "it is known at least since the times of Euclid in ancient Greece that there is an infinitude of prime numbers," Kecker said. "Finding larger and larger prime numbers therefore became a quest for many mathematicians." Currently, the largest known prime number is 2^136,279,841 – 1. To calculate this number, multiply 2 by itself 136,279,841 times, and then subtract 1. The result, also known as M136279841, possesses a whopping 41,024,320 digits, more than 16 million digits more than the previous record holder, called M82589933.

The new largest prime was discovered by amateur researcher and former Nvidia employee Luke Durant, who ran GIMPS on a cloud-based computer network. His efforts required the harnessing of thousands of graphics processing units (GPUs) across 24 data centers in 17 countries — a feat that "ends the 28-year reign of ordinary personal computers finding these huge prime numbers," according to a statement released on the GIMPS website."For a large whole number — say, with a few thousand digits — it becomes more and more time-consuming to check whether or not that number is prime," Kecker said. "Even with the most advanced algorithms and latest supercomputers to run them on, testing whether or not a number is prime could easily exceed a human lifespan."

However, over the years, mathematicians have discovered strategies for finding out if Mersenne numbers are prime, and these methods are far quicker than the techniques used for other kinds of prime numbers. Until 2018, GIMPS discovered a new Mersenne prime about every other year. "It is almost like waiting for a volcanic eruption after a long period of inactivity — although one expects the next one to happen any time, one never knows when it strikes again, if it ever strikes again," Kecker said.

Journal：livescience

Title：What is the largest known prime number?（Oct 24, 2024）

Category：Mathematics

A major difference between real atoms and prime numbers is that the number of different types of stable atoms is finite. 

真实原子和素数之间的一个主要区别是不同类型的稳定原子的数量是有限的。

The mind is always the dupe of the heart.

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