Berikut pemetaan (mapping) angka Delapanpuluh Sembilan (89) ke piramida data dari diagram berupa konsep, detil bagan dan modul² yang dipakai sebagai dasar pemrograman.
Sebelum masuk ke detail, berikut ini daftar keistimewaan angka 89 menurut wikipedia:
- 89 adalah: bilangan prima 24, setelah 83 dan sebelumnya 97 .
- sebuah prime Chen
- sebuah prime Pythagoras
- perdana terkecil Sophie Germain untuk memulai rantai Cunningham dari jenis pertama dari enam istilah, {89, 179, 359, 719, 1439, 2879}.
- sebuah Eisenstein prima tanpa bagian imajiner dan bagian nyata dari bentuk 3 n - 1 .
- angka Fibonacci dan dengan demikian juga merupakan Fibonacci prima .
- Beberapa digit pertama dari timbal baliknya bertepatan dengan urutan Fibonacci karena identitas
- angka Markov, muncul dalam solusi untuk persamaan Markov Diophantine dengan angka Fibonacci indeks aneh lainnya.
- M 89 adalah perdana Mersenne ke-10 .
- Meskipun 89 bukan nomor Lychrel di basis 10, itu tidak biasa bahwa dibutuhkan 24 iterasi dari kebalikan dan menambahkan proses untuk mencapai palindrome . Di antara angka-angka non-Lychrel yang diketahui dalam 10.000 integer pertama, tidak ada angka lain yang mengharuskan banyak atau lebih iterasi. Palindrom yang dicapai juga luar biasa besar.
Berikut ini keistimewaan² lainnya dari Prime Curios!
- 89 is the fifth Fibonacci prime.
- 89 and 97 are the first pair of consecutive primes differing by 8.
- The smallest composite-digit prime.
- 12 x 34567 + 89 is a 9-digital prime expression.
- The smallest Sophie Germain prime to start a Cunningham chain of length 6 (1st kind): (89, 179, 359, 719, 1439, 2879).
- Two to the power 89, minus one, was first proved prime by a man whose last name was Powers.
- 89 = 8 + 92.
- 89 is the smallest circular-digit prime.
- 22 + 33 + 55 + 77 + 1111 + ... + 8989 is prime.
- The reciprocal of the Fibonacci prime number 89 starts out 0.011235... (generating the first five Fibonacci numbers).
- The concatenation of all odd primes starting from 89 and counting in reverse is prime
- M89 begins with digits 61 89. Note the greatest integer function of the natural log of M89 is 61.
- (88*99) is congruent to 8*9 (mod 89).
- 89 is the largest Fibonacci number occurring in natural floral arrangements as the most common number of petals of the Michaelmas daisy (asteraceae family).
- The smallest multidigit prime p such that the sum of digits raised to consecutive powers (i.e., 8^1 + 9^2) is equal to p itself
- 89# - 1 is prime.
- Hugo Steinhaus (1887-1972) proved that if you take any positive integer, find the sum of the squares of its digits, and then repeat; that you will either come to 1 or the cyclic sequence 145, 42, 20, 4, 16, 37, 58, 89.
- 89 is the prime among two-digit numbers that requires the most reverse-and-adding to become a palindrome.
- The smallest holey prime.
- 89 is the smallest prime (indeed the smallest positive integer) whose square (7921) and cube (704969) are likewise prime upon reversal.
- The longest verse in the KJV Bible is Esther 8:9 with 89 plus one words.
- 89 is the larger prime factor of 2^11-1, the smallest composite Mersenne number with prime exponent. [Terr]
- The smallest prime for which the sum of all odd primes less than or equal to it is a square.
- 89 is the smallest prime that is changed into a composite number if any digit is deleted
- 89 = 8*9 + 8+9.
- 89 is the smallest number whose binary and octal representations are all different and all prime if read in decimal. I.e., 1011001 and 131 are all prime. Besides, 89 itself and the hexadecimal representation 59 are also prime.
- The smallest prime formed by the concatenation of consecutive perfect powers in ascending order.
- Choose two 2-digit numbers of the form n = a multiple of ten and n - 1. Now reverse the digits of these two numbers and subtract the smaller from the larger. The result is always 89. For example: 29 and 30 gives 92 - 3 = 89, 89 and 90 gives 98 - 9 = 89.
- 89 = 9+8+7+6+5+4+3+2+1+2+3+4+5+6+7+8+9.
- 89 is the atomic number of Actinium, the first in the list of chemical elements alphabetically ordered. Note the appropriate use of the phrase "atomic number" which literally means "number that cannot be split." [Beedassy]
- The only two-digit prime p such that 2^p + p is prime. [Silva]
- The only prime formed from unrepeated composite digits. [Silva]
- 89 = prime(phi(8)*phi(9)) = prime(phi(sigma(89))), so phi(sigma(89)) = phi(8)*phi(9).
- The largest positive integer that cannot be expressed as the sum of four pentagonal numbers. Its rightmost digit is the smallest positive integer with this property.
- The 5th Fibonacci prime can be expressed by the first 5 integers raised to the first 5 Fibonacci numbers: 1^1 + 2^5 + 3^3 + 4^1 + 5^2.
- 289-1 = 618970019642690137449562111 is the smallest pandigital Mersenne prime
- Is 89 a prime number?
- The largest known prime p with the property that when writing down all the natural numbers from 0 to p one uses the same number of even and odd digits.
- 89 is a common octane rating for gasoline in the United States
- The smallest prime p such that the number "pp" has a square of the form "XXYY": 89892 = 80802121.
- Y-89 is the only naturally occurring stable isotope of Yttrium.
- The larger of only two double-digit primes that does not produce a prime by adding a digit to it. (There is no prime "89d"). The smaller such prime is 53
- The smallest prime that can be written as sum of two powers in five ways.
- The only prime of form p^4+8 for p a prime, (p=3)
- The only double-digit prime that can be written as p*q+r in seven ways, where p, q, r are distinct primes, i.e., 89 = 2*3+83 = 2*5+79 = 2*11+67 = 2*23+43 = 2*29+31 = 2*41+7 = 2*43+3.
- There are exactly one thousand prime numbers between one and 89 squared.
- 89 is the smallest prime that is a different number when turned upside down (in this case 68), which is the sum of the first n strobogrammatic numbers, i.e., 0+1+8+11+69 = 89. Does there exist a strobogrammatic number that is the sum of the first n strobogrammatic numbers?
- The only non titanic prime of form n!-n#-1, (n=5).
- 89 minus 8 is the square of 9. Curiously, 89 plus 8 is the next prime after 89.
- 89^89 is the smallest n^n that contains the ten digits a distinct number of times each
- There are 89 three-digit isolated (i.e., not part of a twin prime pair) prime numbers.
- If A = 1, B = 6, C = 1, D = 8, ... , (using the digits of the Golden Ratio), then 'MERSENNE PRIME NUMBER' = 89; a Mersenne prime exponent that Mersenne himself missed!
- 89 is the last two digits of what Gauss referred to as "a measurable infinity," i.e., 9^(9^(9^9)).
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1 | 1 | 5
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2 | 6 | 14
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3 | 15 | 16
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4 | 17 | 20
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5 | 21 | 26
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6 | 27 | 30
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