Numbers 8,000,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

8,000,000,000 8,100,000,0008,200,000,0008,300,000,0008,400,000,000

8,500,000,0008,600,000,0008,700,000,0008,800,000,000 – 8,900,000,000

All Numbers[1B] – [2B] – [3B] – [4B] – [5B] – [6B] – [7B] – [8B]  – [9B]  & [10B]

1  - 10 - 100  - 1000 - 10,000 - 100,000 - 1M - 10M - 100M1B10B - 100B - 1T - 10T - 100T - 1Q ...

8,000,000,000, 8,000,000,008, 8,000,000,800 & 8,000,000,808

[Language & Math.]  The first numbers in the list of numbers sorted by the English alphabetical order are: eight (8), eight billion (8,000,000,000), eight billion eight (8,000,000,008), eight billion eight hundred (8,000,000,800), eight billion eight hundred eight (8,000,000,808)… 

(See also Numbers 8,800,000,000s and References [3])

 

8,000,000,003

[Math.]   (Sequence of numbers 80…032 = 640…0480…09).

80000000032 = 64000000048000000009 = (–6+4–00000004+8,000,000,009)2.

 

8,000,000,005

[Math.]   (Sequence of numbers 80…052 = 640…080…025).

80000000052 = 64000000080000000025 =  (6+4+0000000+8000000002+5)2.

 

8,000,000,008

[Math.]   The number 8,000,000,008 = 23×7×11×13×19×52,579 has 8 prime factors.

 

8,011,532,460

[Math.]   Two consecutive sums of consecutive square numbers:

8,011,532,460 = 104402+…+105122 = 105132+…+105842.

 

8,014,367,529

[Math.]   895232 = 8,014,367,529, a square number using each of 10 digits 0-9 once. (The 74th of 87 such numbers).

 

8,018,018,849 & 8,018,018,851

[Language & Math.]  The number 8,018,018,851 is the first prime number in the list of prime numbers sorted by the English alphabetical order, whose twin prime number, 8,018,018,849 (eight billion eighteen million eighteen thousand eight hundred forty nine), surprisingly, is the very next prime number in the list.

(See also Numbers 8,800,000,000s and References [3])

 

8,018,018,851

[Language & Math.]  The number 8,018,018,851 was claimed by Donald Knuth as the first prime number in the list of prime numbers sorted by the English alphabetical order, eight billion eighteen million eighteen thousand eight hundred fifty one. It is true if number 800 is preferably written as “eight-hundred”, instead of “eight hundred”.

(See also Numbers 8,800,000,000s and References [3])

 

 

8,024,024,008

[Math.]  (Sequence of numbers 20…02).

20023 = 8,024,024,008 = (–8+02402–400+8)3.

 

8,041,784,976

[Math.]   Sum of the first 423 cube numbers:

13+…+4233 = 8,041,784,976 = (1+2+…+423)2 = 89,6762.

 

x,yzw,abc,def

[Math.]  For any x,yzw = 1000 to 9999, there are always six 6-digit numbers abc,edf such that x,yzw +abc,def is equal to one of 6 digit-rotations of 142,857 and the number x,yzw,abc,def is a multiple of 142,857.

 

 For any x,yzw = 1000 to 9999, there are always twelve 6-digit numbers abc,edf such that x,yzw +abc,def is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number x,yzw,abc,def is a multiple of 76,923.

 

 

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References [3]: Conway & Guy, the Book of Numbers, p.15, 1996.