Numbers 440,000,000,000s
441,066,000,384

[Math.]    Sum of the first 1152 cube numbers:

13+…+11523 = 441,066,000,384 = (1+…+1152)2 = 664,1282.

442,598,808,961

[Math.]    Sum of the first 1153 cube numbers:

13+…+11533 = 442,598,808,961 = (1+…+1153)2 = 665,2812.

444,000,999,555 & 444,000,999,556

[Math.]

642 = 4096 = 4095+1

66342 = 44009956 = 44009955+1

666,3342 = 444,000,999,556 = 444,000,999,555+1

666633342 = 4444000099995556 = 4444000099995555+1

66666333342 = 44444000009999955556 =  44444000009999955555+1

6666663333342 = 444444000000999999555556 = 444444000000999999555555+1.

444,135,609,225

[Math.]    Sum of the first 1154 cube numbers:

13+…+11543 = 444,135,609,225 = (1+…+1154)2 = 666,4352.

444,442,222,224

[Math.]   444,442,222,224 = 666,666×666,664. (See more below)

444,442,222,225

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

444,442,222,225

[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.

666,6652 = 444,442,222,225 & 444,442+222,225 = 666,667 = 666,665+2.

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

444,443,555,556

[Math.]

121×(1+2+1) = 484 = 222

12,321×(1+2+3+2+1) = 110,889 = 3332

1,234,321×(1+2+3+4+3+2+1) = 19,749,136 = 4,4442

123,454,321×(1+2+3+4+5+4+3+2+1) = 3,086,358,025 = 55,5552

12,345,654,321×(1+2+3+4+5+6+5+4+3+2+1) = 444,443,555,556 = 666,6662

1,234,567,654,321×(1+2+3+4+5+6+7+6+5+4+3+2+1) =

= 60,493,815,061,729 = 7,777,7772

123,456,787,654,321×(1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) =

= 7,901,234,409,876,544 = 88,888,8882

12,345,678,987,654,321×(1+2+3+4+5+6+7+8+9 +8+7+6+5+4+3+2+1) =

= 999,999,998,000,000,001 = 999,999,9992.

444,444,000,000

[Math.]  The square root of the number formed by n digits 4 followed by n digits 0 starts with n digits 6, decimal point, and n digits 3:

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…

4444444440000000001/2 = 666666666.3333333332…

44444444440000000001/2 = 6666666666.33333333332…

4444444444400000000001/2 = 66666666666.333333333332…

444444444444000000000001/2 = 666666666666.3333333333332…

444,444,222,222

[Math.]    444,444,222,222 = 666,666×666,667.  (See more below)

444,444,888,888

[Math.]    444,444,888,888 = 666,666×666,668.  (See more below)

444,444,888,889

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

444,445,555,554

[Math.]   444,445,555,554 = 666,666×666,669. (See more below)

445,676,408,100

[Math.]   Sum of the first 1155 cube numbers:

13+…+11553 = 445,676,408,100 = (1+…+1155)2 = 667,5902.

447,221,212,516

[Math.]  Sum of the first 1156 cube numbers:

13+…+11563 = 447,221,212,516 = (1+…+1156)2 = 668,7462.

448,345,497,600

[Math.]  The order of the 13th sporadic group: Suzuki group Suz.

448,770,029,409

[Math.]  Sum of the first 1157 cube numbers:

13+…+11573 = 448,770,029,409 = (1+…+1157)2 = 669,9032.

448,944,221,089

[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.

444,442,222,224, 444,444,222,222, 444,444,888,888, 444,445,555,554 &

444,448,888,884

[Math.]

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

...

 666666×666661 = 444440,222226 666666×666669 = 444445,555554 666666×666663 = 444441,555558 666666×666670 = 444446,222220 666666×666664 = 444442,222224 666666×666671 = 444446,888886 666666×666666 = 444443,555556 666666×666672 = 444447,555552 666666×666667 = 444444,222222 666666×666674 = 444448,888884 666666×666668 = 444444,888888 666666×666675 = 444449,555550

… (generalizable pattern) ...