Numbers 440,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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442,224 & 444,222 & 444,888 & 445,554 & 448,884

[Math.] 

66×64 = 4224

66×67 = 4422

66×68 = 4488

66×69 = 4554

66×74 = 4884

 

666×661 = 440,226

666×666 = 443,556

666×669 = 445,554

666×672 = 447,552

666×663 = 441,558

666×667 = 444,222

666×670 = 446,220

666×674 = 448,884

666×664 = 442,224

666×668 = 444,888

666×671 = 446,886

666×675 = 449,550

… (generalizable pattern) …

 

442,225

[Math.]  Repeatedly inserting number 42 between the digits 4 and 2 in the square number 4225 = 652 yields other squares 442225 = 6652, 44422225 = 66652, 4444222225 = 666652, 444442222225 = 6666652

 

[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.

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

 

442,481

[Math.]   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, nontrivially. (Fermat’s Last Theorem is a special case for only 2 terms).

 

443,520

[Math.]  The order of the 4th sporadic group: Mathieu group M22.

 

 [Math.]  Sum (in degrees) of all internal angles of a 2466-side polygon.

 

443,556

[Math.]  Sum of the first 36 cube numbers:

13+23+…+353+363 = 443,556 = (1+2+…+35+36)2 = 6662.

 

444,000

[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...

...

 

444,883

[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.

 

444,889

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

 

447,678

[Math.]  Two consecutive sums of consecutive numbers: 5776+…+5852 = 5853+…+5928 = 447,678.

 

448,944

[Math.]  108,878,221,089 = (108878+221089)2 = 3299672 and 448,944,221,089 = (448944+221089)2 = 670,0332 and 329967+670033 = 1,000,000.

 

449,065

[Math.]  A Carmichael number: 449,065 = 5×19×29×163.