Numbers 6,600,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

6,000,0006,100,0006,200,0006,300,0006,400,000

6,500,0006,600,0006,700,0006,800,0006,900,000

All Numbers  &  [100K &  [1M]  - [2M]  - [3M] - [4M]  - [5M]  - [6M]  - [7M]  - [8M]  -  [9M]   &  [10M]

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6,615,378

[Math.]  076,923×86 = 6,615,378 and 6+615,378 = 615,384, a digit-rotation of 153,846 = 076,923×2.

 

6,625,109

[Math.]  The 9th square number that is the sum of squares of 2 consecutive numbers: 6,625,1092 = 43,892,069,261,881 = 4,684,6592+4,684,6602. 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:

(4,684,659, 4,684,660, 6,625,109) is the 9th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

 

6,644,672 

[Math.]  6,644,672 = (6+64+46+72)3 = 1883.

 

6,666,665

[Math.]  Repeatedly inserting numbers 42 between the digits 4 and 2 in the square number 4225 = 652 yields other squares 442225 = 6652, 44422225 = 66652, 4444222225 = 666652, 444442222225 = 6666652, 44,444,422,222,225 = 6,666,6652...

 

[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.

6,666,6652 = 44444422222225 & 4444442+2222225 = 6,666,667 = 6,666,665+2.

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

 

6,666,666.33333332…

[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...

 

6,666,667

[Math.] 

3333333,6666667,0000000 = 3,333,3333+6,666,6673+00000003

3333333,6666667,0000001 = 3,333,3333+6,666,6673+00000013. (Generalizable)

 

[Math.]  

133,333,346,666,667 = 13,333,3342–6,666,6672 =

= (13333334+6666667)×6666667. (Generalizable)

 

6,666,667

[Math.] 

333,333,400,000,006,666,667 = 33333343+00000003+66666673.

(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

 

6,666,668

[Math.]  33,333,346,666,668 = 6,666,6682–3,333,3342 = (3333334+6666668)×3333334.

 

6,680,025

[Math.]  A pair of amicable numbers (6377175, 6680025).

 

6,692,301

[Math.]  076,923×87 = 6,692,301 and 6+692,301 = 692,307, a digit-rotation of 076,923.

 

6,666,661, 6,666,663, 6,666,664, 6,666,666, 6,666,667, 6,666,668 & 6,666,669

6,666,670, 6,666,671, 6,666,672, 6,666,674 & 6,666,675,

[Math.]   

66×64 = 4224

66×67 = 4422

66×68 = 4488

66×69 = 4554

66×74 = 4884

6666666×6666661 = 44444402222226

6666666×6666669 = 44444455555554

6666666×6666663 = 44444415555558

6666666×6666670 = 44444462222220

6666666×6666664 = 44444422222224

6666666×6666671 = 44444468888886

6666666×6666666 = 44444435555556

6666666×6666672 = 44444475555552

6666666×6666667 = 44444442222222

6666666×6666674 = 44444488888884

6666666×6666668 = 44444448888888

6666666×6666675 = 44444495555550

… (generalizable pattern) …