Numbers 1,000,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

1,000,000,0001,100,000,0001,200,000,0001,300,000,0001,400,000,000

1,500,000,0001,600,000,0001,700,000,0001,800,000,000 – 1,900,000,000

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 ...

1,000,000,000 (separate page)

 

1,000,000,001

[Math.]

 1,001 = 11×91

 1,000,001 = 101×9901

 1,000,000,001 = 1,001×999,001

 1,000,000,000,001 = 10,001×99,990,001

 1,000,000,000,000,001 = 100,001×9,999,900,001

1,000,000,000,000,001 = 100,001×9,999,900,001

1,000,000,000,000,000,001 = 1,000,001×999,999,000,001

1,000,000,000,000,000,000,001 = 10,000,001×99,999,990,000,001

1,000,000,000,000,000,000,000,001 =

= 100,000,001×9,999,999,900,000,001

1,000,000,000,000,000,000,000,000,001 =

= 1,000,000,001×999,999,999,000,000,001

 

[Math.]   1,000,000,001 = 10003+0003+0013.

 

[Math.]  1,000,000,0012 = 1,000,000,002,000,000,001 = (1000000002–000000001)2

1,000,000,0013 = 1,000,000,003,000,000,003,000,000,001 =

= (1000000003–000000003+000000001)3

 

1,000,000,002

[Math.]   (Sequence of numbers 10…02 & odd powers)

1,000,000,0023 = 1,000,000,006,000,000,012,000,000,008 =

= (1000000006–000000012+000000008)3

 

1,000,000,003

[Math.]  (Sequence of numbers 10…033 = 10…09,0…27,0…27). 

1033 = 1092727, 10033 = 1,009,027,027,…, 1,000,000,0033 =

= 1000000009,000000027,000000027…

 

1,000,000,004

[Math.]   (Sequence of numbers 10…044 = 1,00…16,00…96,0…256, 0…256).

10044 = 1,016,096,256,256,…, 1,000,000,0044 =

= 1,000000016,000000096,000000256,000000256…

 

1,000,000,007

[Math.]   The smallest (10-digit) prime number greater than 1 billion.

 

1,000,000,009

[Math.]   A prime number. All numbers 19, 109, 1009, 10009 are prime and the next is 1,000,000,009.

 

[Math.]   (Sequence of numbers 10…09).

10000000092 = 1000000018000000081 = (1000000018–0000000–8–1)2.

 

1,000,000,011

[Math.]   (Sequence of numbers 10…0112 = 10…022…121).

1,000,000,0112 = 1000000022000000121 = (1,000,000,022–00000012+1)2.

 

1,000,000,014

[Math.]   (Sequence of numbers 10…0142 = 10…028…196).

1,000,000,0142 = 1,000,000,028+0000001–9–6)2.

 

1,000,000,058

[Math.]   (Sequence of numbers 10…0582 = 10…01160…03364).

1,000,000,0582 = 1000000116000003364 = (1000000116+00000+3+3–64)2.

 

1,000,000,078

[Math.]   (Sequence of numbers 10…0782 = 10…01560…06084).

1,000,000,0782 = 1000000156000006084 = (1,000,000,156+000006–084)2.

 

1,000,006,281

[Math.]   A triangular number (sum of all integers from 1 to 44721): 1,000,006,281 = 1+2+…+44720+44721.  The first triangular number greater than 1 billion.

 

1,000,014,129

[Math.]   The smallest 10-digit square number = 316232.

 

1,000,165,033

[Math.]   1,000,165,033 = 10003+163+503+333. (Generalizable)

 

1,000,203,876

[Math.]   Sum of the first 251 cube numbers:  

13+…+2513 = 1,000,203,876 = (1+2+…+251)2 = 31,3752.

 

1,000,340,067

[Math.]   1,000,340,067 = 10003+343+003+673. (Generalizable)

 

1,000,341,067

[Math.]   1,000,341,067 = 10003+343+103+673. (Generalizable)

 

1,000,520,885

[Math.]   A pyramidal number (sum of all squares of integers from 1 to 1442): 1,000,520,885 = 12+22+…+14412+14422The first pyramidal number greater than 1 billion.

 

1,001,000,000--1,050,999,999 (separate page)

 

1,051,000,000--1,099,999,999 (separate page)

 

1,086,823,089 & 1,098,910,989 & 1,099,999,989

[Math.]

(*)   1089×9 = 9,801 = 992 & 1089×9801 = 10,673,289 = 32672

1089…1089×9 = 9801…9801  & 1089…1089×9801…9801  = 3267…32672

 

(**)  10989×9 = 98901 & 10989×98901 = 1,086,823,089 = 329672

10989…10989×9 = 98901…98901 & 10989…10989×98901...98901 = 32967…329672

 

(***)   1099999989×9 = 9899999901 & 1099999989×9899999901 = 32999999672

1099999989…1099999989×9 = 9899999901…9899999901 &

1099999989…1099999989×9899999901...9899999901 = 329999967…32999999672

 

(****)  109…989×9 = 989…901 & 109...989×989…901 = 329…9672

 109…989×9 = 989…901 & 109…989×989…901 = 329…9672… &

109…989…109…989×989…901...989…901 = 329…967…329…9672

...

 

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 x,yzw,abc,def is a multiple of 76,923.