Numbers 2,100,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

2,000,000,000 2,100,000,0002,200,000,0002,300,000,0002,400,000,000

2,500,000,0002,600,000,0002,700,000,0002,800,000,000 – 2,900,000,000

[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 ...

2,106,037,780

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

2,106,037,780 = 61052+…+61602 = 61612+…+62152.

2,109,876,543

[Math.]   2,109,876,543, 2,109,876,543×2 = 4,219,753,086 and 2,109,876,543×4 = 8,439,506,172 are all pan-digital numbers. Hence, a pan-digital number factorization: 4,219,753,0862 = 2,109,876,543×8,439,506,172.

2,121,155,136

[Math.]   Sum of the first 303 cube numbers:

13+…+3033 = 2,121,155,136 = (1+2+…+303)2 = 46,0562.

2,121,212,121

[Math.]   508,853,9892 = 258,932,382,121,212,121 and

1,318,820,8812 = 1,739,288,516,161,616,161.

2,147,483,647

[Math.]   Number 31 is the 3rd Mersenne prime number, 25–1 and is a Mersenne exponent: 231–1 = 2,147,483,647 is the 8th Mersenne prime number. Hence, 231–1 is the (3rd) double Mersenne number.

2,149,249,600

[Math.]   Sum of the first 304 cube numbers:

13+…+3043 = 2,149,249,600 = (1+2+…+304)2 = 46,3602.

2,151,239,746

[Math.]   A Markov number.

2,170,348,569

[Math.]   465872 = 2,170,348,569, a square number using each of 10 digits 0-9 once. (The 19th of 87 such numbers).

2,177,622,225

[Math.]   Sum of the first 305 cube numbers:

13+…+3053 = 2,177,622,225 = (1+2+…+305)2 = 46,6652.

2,197,530,864

[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.

2,197,821,978 & 2,199,999,978

[Math.]

(*)   8712 = 2178×4 & 8712×2178 = 18,974,736 = 43562 (= 664)

8712…8712 = 2178…2178×4 & 8712…8712×2178…2178 = 4356…43562

(**)   87912 = 21978×4 & 21978×87912 = 1,932,129,936  = 439562

87912…87912 = 21978…21978×4 & 21978…21978×87912…87912 = 43956…439562

(***)   8799999912 = 2199999978×4 & 2199999978×8799999912 = 43999999562

8799999912…8799999912 = 2199999978…2199999978×4 &

2199999978…2199999978×8799999912…8799999912 = 4399999956…43999999562

(****)   879…912 = 219…978×4 & 219…978×879…912 = 439…9562

879…912…879…912 = 219…978…219…978×4 &

219...978...219...978×879...912...879...912 = 439...956...439...9562

...

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.