Numbers 210,000s


A page of the Numeropedia - the Special Encyclopedia of Numbers

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210,630

[Math.]  Two consecutive sums of consecutive numbers: 3481+…+3540 = 3541+…+3599 = 210,630. 

 

212,625

[Math.]  212,625 = 17×35×53×71.

 

213,018

[Math.]  213,018,248,521 = (213,018+248,521)2 = 461,5392 and 289,940,248,521 = (289940+248521)2 = 538,4612 and 461,539+538,461 = 1,000,000.

 

213,444

[Math.]  213,444 = (21–3+444)2 = 4622.

 

216,091

[Math.]  A prime number.

A Mersenne exponent: 2216091–1 is the 31st Mersenne prime number.

 

216,225

[Math.]  Sum of the first 30 cube numbers:

13+23+33+…+283+293+303 = 216,225 = (1+2+3+…+28+29+30)2 = 4652.

 

217,124

[Math.]  101,558,217,124 = (101,558+217124)2 = 318,6822 and 464,194,217,124 = (464194+217124)2 = 681,3182 and 318682+681318 = 1,000,000.

 

217,519

[Math.]  A prime number.  

4424814 = 4145604+2175194+958004. The smallest counter-example to disprove Euler’s conjecture that it always requires at least n terms (of nth power) to sum to an nth power, non-trivially. (Fermat’s Last Theorem is a special case for only 2 terms).

 

217,930

[Math.] 217,930,248,900 = (217,930+248,900)2 = 466,8302 and 284,270,248,900 = (284270+248900)2 = 533,1702 and 466,380+533,170 = 1,000,000.

 

218,751

[Math.]  Its odd powers end with 218,751. Its even powers end with 000,001.

 

219,876

[Math.]  Number 0,219,876 misses 3 digits 3, 4 and 5 in 10 digits 0-9.

0,219,876×2 = 0,439,752 misses 3 digits 6, 8 and 1 (modulo 9).

 

219,978

[Math.] 

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

87128712 = 21782178×4 & 87128712×21782178 = 435643562

 

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

8791287912 = 21978…21978×4 & 21978…21978×87912…87912 = 43956…439562

 

(***)   879912 = 219978×4 & 219978×879912 = 193,561,281,936 = 4399562

879912879912 = 219978219978×4 &

219978219978×879912879912 = 4399564399562

 

(****)   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.