Numbers 4,400,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

4,100,000,0004,200,000,0004,300,000,0004,400,000,000

4,500,000,0004,600,000,0004,700,000,0004,800,000,000 – 4,900,000,000

[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 ...

4,403,471,114

[Math.]   4,403,471,114 = 21+42+63+84+105+126+147+168.

4,412,944,900

[Math.]   Sum of the first 364 cube numbers:

13+…+3643 = 4,412,944,900 = (1+2+…+364)2 = 66,4302.

4,444,222,224 (see below)

4,444,222,225

[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.

66,6652 = 4,444,222,225 & 44,442+22,225 = 66,667 = 66,665+2.

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

[Math.]   Repeatedly inserting number 42 between the digits 4 and 2 in the square number 4225 = 652 yields other squares 442225 = 6652, 44422225 = 66652, 444222225 = 666652, 44442222225 = 6666652

4,444,400,000

[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…

...

4,444,422,222

[Math.]   4,444,422,222 = 66666×66667.

4,444,488,883

[Math.]   A prime number.

Repeatedly inserting number 48 into the middle of number 43 gives a sequences of prime number: 43, 4483, 444,883, 44,448,883 and 4,444,488,883.

4,444,488,888

[Math.]   4,444,488,888 = 66666*66668.

4,444,488,889

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

4,444,555,554

[Math.]   4,444,555,554 = 66666*66669.

4,461,572,025

[Math.]   Sum of the first 365 cube numbers:

13+…+3653 = 4,510,599,921 = (1+2+…+365)2 = 66,7952.

4,464,934,240

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

4,464,934,240 = 82562+…+83202 = 83212+…+83842.

4,444,222,224, 4,444,422,222, 4,444,488,888, 4,444,555,554 & 4,444,888,884

[Math.]

 66×64 = 4224 66×67 = 4422 66×68 = 4488 66×69 = 4554 66×74 = 4884

 66666×66661 = 4444022226 66666×66669 = 4444555554 66666×66663 = 4444155558 66666×66670 = 4444622220 66666×66664 = 4444222224 66666×66671 = 4444688886 66666×66666 = 4444355556 66666×66672 = 4444755552 66666×66667 = 4444422222 66666×66674 = 4444888884 66666×66668 = 4444488888 66666×66675 = 4444955550

… (generalizable pattern) …

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.