As human beings, we may be far from perfect. Even our mathematical celebrations, like Pi Day, are mere approximations. But there are a few mathematical quantities out there that really are perfect. And today, June 28th, I'd like to share with you a celebration we should all be able to partake in: perfect number day! Show
 Most numbers are deficient, in the sense that if you added up all their divisors (other than themselves), you get a number less than the original one you began with. A few of them -- about 24.8% of the countable numbers -- wind up being abundant, or with a number greater than the original one you began with. But a select few of them -- with only 48 known so far -- are perfect. Go read the whole story of them here! Tags math
"It has been proven that all the even perfect numbers that exist are of the form (2^n - 1)" I think there must be a typo, or other mistake in this sentence, as (2^n-1) seems definitely odd to me. Unless there's a definition of "even perfect number" that I somehow overlooked. Sorry, that should have read "It has been proven that all the even perfect numbers that exist are of the form that are generated by Mersenne primes that follow (2^n - 1)," and that has been fixed. Today is Perfect Number Day! A Perfect Number is a number whose factors add up to the same number. For example, 6 is a Perfect Number because the factors of 6 (= 1+2+3) add up to 6. The next Perfect number is 28 (= 1+2+4+7+14). Yes, you guessed it right! That’s why 6/28 i.e. 28th June is considered Perfect Number Day! Advertisement Share this:Like this:Like Loading... RelatedA number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28. Why June 28th is the only perfect day of the year?June 28 is a perfect date because 6 and 28 are both perfect numbers, numbers whose divisors add up to themselves. The numbers 1, 2, and 3 are the three divisors of 6 (other than 6 itself) and 1+2+3=6. Likewise, 28=1+2+4+7+14. Euclid's Elements contains the first known theorem about perfect numbers.What number is the most perfect?In number theory, a perfect number is a positive integer that is equal to the sum of its positive factors, excluding the number itself. The most popular and the smallest perfect number is 6, which is equal to the sum of 1, 2, and 3. Other examples of perfect numbers are 28, 496, and 8128.What are the perfect number between 1 and 28?The perfect numbers between 1 and 28 are 6 and 28. A perfect number is a number that is the sum of all its factors, not including the number itself.What is the most beautiful number?The number 1.618… goes by many different names. However, mathematicians mostly call it phi. Everywhere around us, we see this beautiful number.Perfect NumberWhich is the powerful number?A number n is said to be Powerful Number if for every prime factor p of it, p2 also divides it. For example:- 36 is a powerful number. It is divisible by both 3 and square of 3 i.e, 9.What is the most weird number?The first few weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, ... (OEIS A006037). An infinite number of weird numbers are known to exist, and the sequence of weird numbers has positive Schnirelmann density.Is 28 a happy number?The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ...Is 28 a friendly number?The numbers known to be friendly are given by 6, 12, 24, 28, 30, 40, 42, 56, 60, ... (OEIS A074902). Friendly numbers have a positive density.Why 28 is not a perfect square?The number 28 is lies between 25 and 36, therefore 28 is not a perfect square of an integer.What is the 1st perfect number?perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.What is the attractive number?A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.What is the amazing number?A number is called amazing if it has exactly three distinct divisors. Example 1: Input: N = 3 Output: 0 Explanation: 3 has only two divisors 1 and 3.So answer is 0.Is June 28 special?June 28, 2022 - NATIONAL PAUL BUNYAN DAY – NATIONAL LOGISTICS DAY – NATIONAL INSURANCE AWARENESS DAY – NATIONAL ALASKA DAY - National Day Calendar.What is so special about 28 June?A Bosnian Serb, Gavrilo Princip, assassinated Archduke Francis Ferdinand of Austria and his wife Sofia in Sarajevo on June 28, 1914, setting off a chain of events that would culminate in a world war by August.Is July 28 special?National Refreshment Day - July 28, 2022 (Fourth Thursday in July) National Waterpark Day. World Hepatitis Day. World Nature Conservation Day.What number is most people's favorite?Math blogger Alex Bellos recently did this, and after polling more than 44,000 people from around the world on his website, he got an answer: The world's favorite number is 7.What is the lucky number for everyone?Seven was the most popular choice for both men and women. The survey revealed some other findings, too.What is everyone's least favorite number?More than any other number, people seemed to pick 0 because they thought it was a clever thing to do, Bellos says. As for the world's “least favorite” number, that would be 110.What type of number is 28?The number 28 is a composite and it should have prime factors.What is the largest happy number?7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487 (sequence A035497 in the OEIS).Is there a sad number?The numbers for which the process of summing up of the squares of its digits ends in 1 are happy numbers. On the other hand, numbers that don't end in 1 are called unhappy or sad numbers. Let's look at the examples below to understand the concept behind it better. Example 1:- 23 is a happy number.What is the first boring number?There's an old math paradox that says that all natural numbers are interesting, since otherwise there would have to be a smallest uninteresting number, and that in itself is pretty interesting.What are boring numbers?According to the book, a positive number is called boring if all of the digits at even positions in the number are even and all of the digits at odd positions are odd. The digits are enumerated from left to right starting from 1.What is the master number?In Numerology, the numbers 11, 22, and 33 are so exceptional that they've been dubbed as “Master Numbers.” These profound energies, when combined, embody the three stages of creation: envisioning, creating, and sharing.Is June 28 a perfect day?(That is, if it turns out to be prime.) But for numbers with one or two digits, only two of them are perfect: 6 and 28. Whether you write the month or date first, that makes June 28 the only “perfect” day of the year, a mathematical fact you can enjoy — and, if you like, explore — any time you like!
Why is 28 called a perfect number?This works out because the only improper divisor of a number is the number itself. We see that 28 is still perfect by this definition: Its proper divisors are 1, 2, 4, 7 and 14, its improper divisor is 28, and the sum of all its divisors, 1 + 2 + 4 + 7 + 14 + 28, is 56, which is 2 × 28.
Is the number 28 a perfect number?perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.
What does the 28th of June celebrate maths?Tau comes to the number (6.28) is twice as much as pi (3.14) which is why Tau Day is 6/28.
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Why is June 28 the perfect number day?
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