Numbers 66,000,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

60,000,000,00061,000,000,00062,000,000,000 – 63,000,000,00064,000,000,000

65,000,000,00066,000,000,00067,000,000,00068,000,000,00069,000,000,000

All Numbers  – [1B] –  [10B] –  [20B] – [30B] – [40B] – [50B] – [60B] – [70B] – [80B] – [90B] & [100B]

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

66,256,304,409

[Math.]  Sum of the first 717 cube numbers:

13+…+7173 = 66,256,304,409 = (1+…+717)2 = 257,4032.

 

66,626,450,641

[Math.]  Sum of the first 718 cube numbers:

13+…+7183 = 66,626,450,641 = (1+…+718)2 = 258,1212.

 

66,666,666,664, 66,666,666,666, 66,666,666,667 & 66,666,666,668

[Math.]   

66×64 = 4224

66×67 = 4422

66×68 = 4488

66×69 = 4554

66×74 = 4884

 … (generalizable pattern) … 

66,666,666,666´66,666,666,664 = 4444444444222222222224

66,666,666,666´66,666,666,667 = 4444444444422222222222

66,666,666,666´6,6666,666,668 = 4444444444488888888888

66,666,666,666´66,666,666,669 = 4444444444555555555554.

 

66,666,666,665

[Math.]  Repeatedly inserting numbers 42 between the digits 4 and 2 in the square number 4225 = 652 yields other squares 442225 = 6652, 44422225 = 66652, 444222225 = 666652

 

[Math.]  Square of numbers of similar pattern xxy, where y = x–1.

*  1102 = 012,100 & 012+100 = 112 = 110+2

*  3322 = 110,224 & 110+224 = 334 = 332+2.

Similarly, 3…322 = 1…102…24 & 1…10+2…24 = 3…34 = 3…32+2

*  4432 = 196,249 & 196+249 = 445 = 443+2.

*  6652 = 442,225 & 442+225 = 667 = 665+2.

Similarly, 6…652 = 4…422…25 & 4…42+2…25 = 6…67 = 6…65+2

66,666,666,6652 = 4444444444222222222225 & 44444444442+22222222225 = 66,666,666,667 = 66,666,666,665+2.

*  7762 = 602,176 & 602+176 = 778 = 776+2.

   

66,666,666,666.333333333332... 

[Math.]

401/2 = 6.32…

44001/2 = 66.332…

4440001/2 = 666.3332…

444400001/2 = 6666.33332…

44444000001/2 = 66666.333332…

4444440000001/2 = 666666.3333332…

444444400000001/2 = 6666666.33333332…

44444444000000001/2 = 66666666.333333332…

4444444440000000001/2 = 666666666.3333333332…

44444444440000000001/2 = 6666666666.33333333332...

4444444444400000000001/2 = 66666666666.333333333332...

...

 

66,666,666,667

[Math.]  A prime number.

 33333333333,66666666667,00000000000 =  

= 3,333,333,3333+66,666,666,6673+000000000003

and 33333333333,66666666667,00000000001 =

=  33,333,333,3333+66,666,666,6673+000000000013.

 

13,333,333,333,466,666,666,667 = 133,333,333,3342–66,666,666,6672 =

= (13333333334+66666666667)×66666666667.

 

333,333,333,340,000,000,000,066,666,666,667 =

= 33,333,333,3343+000000000003+66,666,666,6673. (Generalizable)

 

[Math.]  Repeatedly inserting numbers 48 in the middle of the square number 49 yields other squares 4489 = 672, 444889 = 6672, 44448889 = 66672, 4444488889 = 666672

 

66,666,666,668

[Math.]  3,333,333,333,466,666,666,668 = 66,666,666,6682–33,333,333,3342 =

= (33333333334+66666666668)×33333333334.  (Generalizable)

 

66,771,917,766

[Math.]  A triangular number:  1+…+365,436 = 66,771,917,766, which is palindromic.

 

66,998,145,600

[Math.]  Sum of the first 719 cube numbers:

13+…+7193 = 66,998,145,600 = (1+…+719)2 = 258,8402 

 

xy,zwv,abc,def

[Math.]  For any xy,zwv = 10,000 to 99,999, there are always six 6-digit numbers abc,edf such that xy,zwv +abc,def is equal to one of 6 digit-rotations of 142,857 and the number xy,zwv,abc,def is a multiple of 142,857.

 

For any xy,zwv  = 10,000 to 76,922, there are always twelve 6-digit numbers abc,edf such that xy,zwv +abc,def is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xy,zwv,abc,def is a multiple of 76,923.