El Problema Sin Resolver Más Antiguo En Matemáticas
Veritasium en español・2 minutes read
The search for the oldest unsolved mathematical problem involving odd perfect numbers continues, with mathematicians using computers to explore numbers up to 10 to the 2200th power. Various mathematicians like Euclid, Leonard Euler, and Peter Barlow have made significant contributions to understanding perfect numbers and prime numbers.
Insights
- The oldest unsolved mathematical problem, related to odd perfect numbers, has intrigued mathematicians for over 2000 years, with significant contributions from various scholars like Euclid, Euler, and Meren, leading to the discovery of patterns in perfect numbers and prime numbers corresponding to them.
- The ongoing search for odd perfect numbers, despite advanced computational techniques and the discovery of numerous Mersenne primes through projects like GIMPS, highlights the complexity and elusive nature of these numbers, prompting researchers to explore diverse conditions and set lower limits on their potential size in pursuit of a solution.
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Recent questions
What is the oldest unsolved mathematical problem?
Odd perfect numbers
How are perfect numbers defined?
Numbers whose divisors sum up to the number
Who discovered the perfect eighth number?
Leonard Euler
What project led to the discovery of numerous Mersenne primes?
GIMPS project
What is the current status of the search for odd perfect numbers?
Ongoing research with lower size limits explored
Related videos
Summary
00:00
"Oldest Math Problem: Odd Perfect Numbers Mystery"
- The oldest unsolved mathematical problem dates back 2000 years.
- Italian mathematician Pier Georgio Od Freddy included it among four pressing problems in 2000.
- Mathematicians have used computers and revised numbers up to 10 to the 2200th power.
- The problem involves odd perfect numbers, defined as numbers whose proper divisors sum up to the number itself.
- Examples like 6 and 28 are perfect numbers, with 6 being the sum of 1 + 2 + 3 and 28 being the sum of 1 to 7.
- Perfect numbers have one more digit than the previous number and end in alternating digits of 6 and 8.
- Perfect numbers can be represented as the sum of consecutive numbers or consecutive odd numbers to the cube.
- Euclid discovered a pattern in perfect numbers by doubling numbers successively.
- French polymath Marine Meren identified prime numbers corresponding to perfect numbers.
- Leonard Eiler discovered the perfect eighth number by verifying 2 to the 31st - 1 is prime, using the Sigma function to find divisors.
15:52
"Euler's Legacy: Prime Numbers and Powers"
- Sigma function results in an even number when a prime number is raised to the power of 1.
- Sigma function returns an odd number when a prime number is raised to an even power.
- Euler's genius lies in the unique properties of prime numbers raised to odd or even powers.
- Euler's work led to the discovery of even perfect numbers satisfying specific conditions.
- Peter Barlow initially believed Euler's eighth perfect number was the largest, but subsequent discoveries proved him wrong.
- Edward Luca and Frank Nelson made significant contributions to the discovery of Mersenne primes.
- The search for Mersenne primes continued, with George Waltman launching a successful project called GIMPS.
- GIMPS project led to the discovery of numerous Mersenne primes, with participants being recognized for their contributions.
- The quest for odd perfect numbers continues, with researchers setting lower limits on their potential size and exploring various conditions to identify them.
