Mathematically 82

Eighty two (82)

1. It is the product of two primes with the unique property that the sum of digits of 82 is equal to the product of sum of digits of its prime factors.
82 = 2 x 41 and 8+ 2 = 10 = 2 x ( 4 + 1)

2. It can be expressed as the sum of two primes in 5 different ways.
82 = 3 + 79
= 11 + 71
= 23 + 59
= 29 + 53
= 41 + 41

3. It is a 15 gonal number as well as a centered 27- gonal number.

4. Six hexagons can be linked in 82 different ways. A figure made from 6 hexagons is called hexahex. One arrangement is shown here.

5. The atomic number of Lead is 82.

6. On Ternary base it is a Palindrome digits. (10001)3 = (82)10.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Matheamatically 81

Eighty One (81)

1. It is a square number.
9^2 = 81

2. It is the sum of first nine odd integers.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

3. It is the square of sum of its digits. Apart from 0 and 1 it is the only number with this property.
81 = ( 8 + 1)^2

4. It is the fourth power of a number.
3^4 = 81

5. It is the smallest square whose sum of divisors is also a square number. The divisors of 81 are 1, 3, 9, 27 and 81 and their sum is 121 which is a square number.
1 + 3 + 9 + 27 + 81= 121 = 11^2

6. It is the sum of 9 consecutive numbers.
5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 81

7. The fraction 1/ 81= 0.01245679 012345679… is a repeating decimal containing every digits from 0 to 9 except 8.

8. On base 10, it is a Harshad number.

9. It is a heptagonal number as well as centered octagonal number.

10. The atomic number of Thallium is 81.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 80

Eighty (80)

1. It is the product of 5 primes.
80 = 2 x 2 x 2 x 2 x 5

2. It is a semi perfect number. There are several divisors of 80 –1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
Adding some of the divisors we get 80 making it a semi perfect number.
80 = 1 + 4 + 5 + 10 + 20 + 40

3. It is the smallest number with the property that n and n+1 are both product of 4 or more primes.
80 = 2 x 2 x 2 x 2 x 5
81 = 3 x 3 x 3 x 3

4. It can be expressed as the sum of two primes in 4 distinct ways.
80 = 7 + 73 = 13 + 67 = 19 + 61 = 37 + 43

5. It is an abundant number.

6. It is a Harshad number.

7. The atomic number of Mercury is 80.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Matheamatically 79

Seventy Nine (79)

1. It is an odd prime number.

2. It is the sum of three consecutive prime. More interestingly, its reverse 97 is the sum of the reversible prime.
79 = 11 + 31 + 37
97 = 11 + 13 + 73

3. It is a Gaussian prime that can be written in the form of 4n + 3.
79 = 4 x 19 + 3

4. It can be written as the sum of their digits added to the product of their digits.
79 = (7 + 9) + (7 x 9)
In fact, all primes ending with 9 can be expressed as the sum of their digits added to the product of their digits.

5. It is a Pillai prime because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23.

6. The atomic number of Gold is 79.

7. It is the maximal number of regions into which 12 lines divide a plane.

8. It is a 13-gonal as well as 26-gonal number.

9. It is a Kynea number. A Kynea number is an integer written in the form of .
The Kenya numbers are 7, 23, 79, 287, 1087...

10. It is a sexy prime number. Sexy primes are prime numbers that differ by 6.
The first 5 sexy prime pairs are – (5, 11), (7, 13), (11, 17), (13, 19), (17, 23) ---

There are infinite many sexy prime triplets and quadruplets numbers. The sexy prime triplets are three prime numbers that differ by 6 and the same happens with the quadruplets. (7, 13, 19), (17, 23, 29), (31, 37, 43) are the examples of sexy prime triplets whereas (5, 11, 17, 23), (11, 17, 23, 29)... are the example of sexy prime quadruplets.


Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 78

Seventy Eight (78)

1. It is the smallest number which can be written as the sum of four distinct squares in 3 ways.
78 = 1^2 + 2^2 +3^2 + 8^2
= 1^2 + 4^2 + 5^2 + 6^2
= 2^2 + 3^2 + 4^2 + 7^2

2. It is a triangular number.

3. It is the sum of first 12 natural numbers.
1 + 2 + 3 + --- + 12 = 78

4. There are 78 Tarot cards which is used for fortune telling. 56 among them the cards of lesser arcana and 22 are of greater arcana.

5. It can be written as the sum of two consecutive primes.
78 = 37 + 41

6. It is a 27-gonal number.

7. It is divisible by three distinct prime number 2, 3 and 13 which makes it a member of Sphenic number. A Sphenic number is a positive integer having three distinct prime factors.
The first five Sphenic numbers are – 30, 42, 66, 70 and 78.

8. The atomic number of Platinum is 78.

9. The number of chromosomes in canine of DNA is 78.

10. It is an abundant number.


Rajesh Kumar Thakur
rkthakur1974@gmail.com

Matheamatically 77

Seventy Seven (77)

1. It is the product of two odd primes.
77 = 7 x 11

2. It is the sum of first 8 prime numbers.
77 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19

3. Any number that is based on the pattern abcabc will be divisible by 77.
123123 ÷ 77 = 1599

4. It is the largest number that cannot be written as the sum of distinct numbers whose reciprocals add up to 1.
78 = 2 + 6 + 8 + 10 + 12 + 40
1 = ½ + 1/6 + 1/8 + 1/10 + 1/12 + 1/40

5. FORTRAN 77 was a computer programming developed by IBM in 1950.

6. It can be expressed as the sum of squares of three consecutive numbers.
77 = 4^2 + 5^2 + 5^2

7. The atomic number of Iridium is 77.

8. It can be partitioned 39 times with each tern not larger than 2 and 533 times with each term no larger than 2.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 76

Seventy Six (76)

1. It is a Lucas number. The sequence in Lucas also moves like Fibonacci sequence. The numbers in Lucas series are- 1, 3, 4, 7, 11, 18, 29, 47, 76..

2. Sum of 4 consecutive Fibonacci sequence is 76.
8 + 13 + 21 + 34 = 76

3. It can be expressed as the sum of squares of primes.
76 = 32 + 32 + 32 + 72

4. Any power of 76 end with 76. Such numbers whose any power ends with the number itself is called automorphic. There are only two automorphic numbers 25 and 76 that are below 100.

76^2 = 5776 76^3 = 438976
76^4 = 33362176 76^5 = 2535525376

5. The atomic number of Osmium is 76.

6. It is a 14-gonal number.

7. It is a centered 25-gonal number.

8. It is a centered 25-gonal number.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com