Numbers 7,600,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

7,100,000,0007,200,000,0007,300,000,0007,400,000,000

7,500,000,0007,600,000,0007,700,000,0007,800,000,000 – 7,900,000,000

[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 ...

7,645,370,045

[Math.]   The 13th square number that is the sum of squares of 2 consecutive numbers: 5,406,093,0032+5,406,093,0042 = 7,645,370,0452. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 52, 292, 1692, 9852

Or in other words:

(5,406,093,003, 5,406,093,004, 7,645,370,045) is the 13th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

7,654,320,918

[Math.]   One of 27 special permutations of the pan-digital number 1,234,567,890: 123,456,789×62 = 7,654,320,918.

7,668,680,041

[Math.]   Sum of the first 418 cube numbers:

13+…+4183 = 7,668,680,041 = (1+2+…+418) = 87,5712.

7,680,594,321

[Math.]   876392 = 7,680,594,321, a square number using each of 10 digits 0-9 once. (The 69th of 87 such numbers).

7,691,358,024

[Math.]   Number 1,098,765,432 and its multiples:

1,098,765,432×2 = 2,197,530,864; 1,098,765,432×4 = 4,395,061,728;

1,098,765,432×5 = 5,493,827,160; 1,098,765,432×7 = 7,691,358,024 and

1,098,765,432×8 = 8,790,123,456 are all pan-digital numbers.

Hence, there are pan-digital number equalities:

1,098,765,432×4,395,061,728 = 2,197,530,8642

2,197,530,864×8,790,123,456 = 4,395,061,7282.

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.