Ikigai Daily
Menu
WonderScience fact

Prime numbers, whole numbers above 1 that divide exactly only by 1 and by themselves (2, 3, 5, 7, 11 and so on), never run out: however far you count, there is always a larger one. Euclid proved this about 2,300 years ago.

Mathematics

Science

The story behind the card

The proof is in Euclid's Elements, written in Alexandria around 300 BC. Suppose you had a complete list of all the primes. Multiply them all together and add one. The new number leaves a remainder of 1 when divided by any prime on the list, so either it is prime itself or it is divisible by a prime missing from the list. Either way the list was not complete, so the primes can never end. In October 2024 Luke Durant, working with the volunteer project GIMPS, found the largest prime known at the time: 2 to the power of 136,279,841, minus 1, a number with 41,024,320 digits. Primes also help keep online payments secure, because some encryption relies on how hard it is to split a huge number into its prime factors.

Türkçe oku
Asal sayılar, yani 1'den büyük olup yalnızca 1'e ve kendisine tam bölünen tam sayılar (2, 3, 5, 7, 11 gibi), hiçbir zaman tükenmez: Ne kadar ileri sayarsanız sayın, daha büyük bir asal sayı mutlaka vardır. Bunu yaklaşık 2.300 yıl önce Öklid kanıtladı.

Kanıt, MÖ 300 dolaylarında İskenderiye'de yazılan Öklid'in Elementler adlı eserinde yer alır. Bütün asal sayıların eksiksiz bir listesine sahip olduğunuzu varsayın. Hepsini çarpın ve sonuca 1 ekleyin. Elde ettiğiniz sayı, listedeki herhangi bir asala bölündüğünde hep 1 kalanını verir. Demek ki bu sayı ya kendisi asaldır ya da listede olmayan bir asala bölünür. Her iki durumda da liste eksikmiş demektir; yani asal sayılar sonsuza dek sürer. Luke Durant, Ekim 2024'te gönüllülerin yürüttüğü GIMPS projesinde, o güne kadar bilinen en büyük asal sayıyı buldu: 2 üzeri 136.279.841 eksi 1. Bu sayı 41.024.320 basamaklıdır. Asal sayılar internetteki ödemelerin güvenliğinde de iş görür: Bazı şifreleme yöntemleri, çok büyük bir sayıyı asal çarpanlarına ayırmanın ne kadar zor olduğuna dayanır.

Sources and further reading

Background reading: Prime number
Get the mobile appAbout our cards

Related cards

These cards share a subject or reading mode with the card above.

WonderHistory

The Industrial Revolution put the clock in charge of the working day. Before factories, most people worked by daylight, the seasons and the task in hand; from the 1770s, mills such as Richard Arkwright's at Cromford in Derbyshire ran day and night in twelve-hour shifts.

The historian E. P. Thompson traced this change in a famous essay of 1967, “Time, Work-Discipline, and Industrial Capitalism”. Farm and craft work, he argued, had been measured by tasks: milking, harvesting, finishing a piece. Factory work was measured in hours. Cromford Mill, opened in 1771, was the world's first water-powered cotton-spinning mill. It started with about 200 workers, most of them women and children, the youngest only seven. Bells rang at 5 in the morning and 5 in the evening, the gates were shut at exactly 6, and anyone late lost that day's pay and was fined another. In industrial towns, where alarm clocks were not yet cheap or reliable, “knocker-ups” were paid a few pence a week to tap on upstairs windows with long poles.

Ikigai DailyRead card
WonderHistory

Less than 66 years, well within a single lifetime, separate the first powered aeroplane flight from the first Moon landing. Orville Wright flew for 12 seconds and 37 metres on 17 December 1903; Apollo 11 landed on the Moon on 20 July 1969.

The Wright brothers, bicycle makers from Dayton, Ohio, flew near Kitty Hawk, North Carolina, and that first hop was shorter than the wingspan of a Boeing 747. What followed came fast. In 1919 John Alcock and Arthur Brown flew non-stop across the Atlantic; in 1927 Charles Lindbergh did it alone, from New York to Paris; and in 1947 Chuck Yeager flew faster than sound. Orville Wright died in 1948, nine years before the Soviet satellite Sputnik opened the space age. Yuri Gagarin orbited the Earth in 1961, and in July 1969 Neil Armstrong took a scrap of the 1903 Flyer's wood and fabric with him to the Moon.

Ikigai DailyRead card
WonderHistory

The Cold War between the United States and the Soviet Union (1947–1991) was fought mostly without direct battles between the two. They competed instead through weapons, science, sport, films, propaganda and the race into space.

George Orwell used the phrase “cold war” in 1945, and the American journalist Walter Lippmann made it popular in 1947. Because nuclear weapons made open war between the superpowers too dangerous, the rivalry spread into other arenas. After the Soviet Union launched the Sputnik satellite in 1957, the United States passed the National Defense Education Act of 1958 to fund science, maths and language teaching. In 1959, at an American exhibition in Moscow, Vice-President Richard Nixon and the Soviet leader Nikita Khrushchev argued about capitalism and communism in a model kitchen, an exchange remembered as the Kitchen Debate. In 1972 in Reykjavík, the American Bobby Fischer beat the Soviet champion Boris Spassky for the world chess title. The Olympics were boycotted in turn: the United States and many allies stayed away from Moscow in 1980, and most of the Soviet bloc from Los Angeles in 1984.

Ikigai DailyRead card
WonderHistory

The Apollo Guidance Computer, which helped steer astronauts to the Moon, was one of the first computers built from integrated circuits: small silicon chips that each carry several electronic components. Until 1965, Apollo was the biggest user of these new chips.

The computer was designed at the MIT Instrumentation Laboratory from 1962 and built by Raytheon, and one flew in every Apollo command module and lunar module. The chip was still a new invention: Jack Kilby and Robert Noyce had made the first ones in 1958 and 1959. MIT used almost a single type throughout, a simple logic circuit designed by Fairchild Semiconductor, repeated thousands of times. According to the Computer History Museum, Apollo bought some 200,000 of them at 20 to 30 dollars each, and by 1965 the Minuteman missile programme had become the bigger buyer. Orders like these kept the young industry going until prices fell: the average chip cost 50 dollars in 1962 and 2.33 dollars in 1968. The Space Race is often credited with GPS too, but GPS was a separate US Department of Defense project, begun in 1973.

Ikigai DailyRead card
WonderHistory

On 12 April 1961 the Soviet cosmonaut Yuri Gagarin, aged 27, became the first human in space. His Vostok 1 spacecraft circled the Earth once, and the flight lasted 108 minutes from launch to landing.

Gagarin, who had trained as a foundry worker before becoming an air force pilot, was launched from Baikonur, in today's Kazakhstan. As the rocket lifted off he called out “Poyekhali!” (“Let's go!”). His orbit took him as high as 327 kilometres. On the way back he ejected from the capsule about 7 kilometres above the ground and came down by his own parachute near Engels, in the Saratov region, where a farm worker and her granddaughter were the first to meet him. Because the record rules of the day required pilots to land inside their craft, the Soviet Union claimed he had, and admitted the truth only in 1971. Gagarin became famous around the world. He died in a training-jet crash in 1968, aged 34. Since 2011 the United Nations has marked 12 April as the International Day of Human Space Flight.

Ikigai DailyRead card
Next card in the archiveIndian mathematicians were the first to treat zero as a number in its own right, not just a gap or a mark for an empty place. In AD 628 Brahmagupta wrote down rules for adding, subtracting and multiplying with it.Read next →