6,601

[Math.]  The 6th Carmichael number: 6601 = 7×23×41.

 

6,603

[Math.]  Square and cube of number 6603 use different digits:  66032 = 43,599,609 and 66033 = 287,888,218,227.

 

6,611

[Math.]  A Cullen prime number: 6611×26611+1.

 

6,634

[Math.]   642 = 4096 = 4095+1

             66342 = 44009956 = 44009955+1

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

             

 

6,647

[Science]  The melting temperature of carbon (diamond) is about 3550 oC = 6422 oF and of carbon (graphite/amorphous) is 3675 oC = 6647 oF.

 

6,660

[Math.]  Sum (in degrees) of all internal angles of a 39-side polygon.

 

6,663

[Math.]  The 6663rd prime number is 66,863.

 

6,665

[Math.]  Repeatedly inserting numbers 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.

6,6652 = 44422225 & 4442+2225 = 6,667 = 6,6665+2.

Similarly, 6…652 = 4…422…25 & 4…42+2…25 = 6…67 = 6…65+2.

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

 

6,666

[Phone]  The number to key in text messaging on telephone keypad for number 6.

 

6666.33332

[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…

 

6,667

[Math.]  333,366,670,000 = 3,3333+6,6673+00003.

             333,366,670,001 = 3,3333+6,6673+00013.

 

             333,400,006,667 = 33343+00003+66673 and

             333,401,006,667 = 33343+01003+66673.

 

133,346,667 = 13,3342–66672 = (13334+6667)×6667, where 13334 = 6667×2.

 

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

 

6,668

[Math.]  33,346,668 = 66682–33342 = (3334+6668)×3334, where 6668 = 3334×2.

 

6,670

[Math.]  A triangular number (sum of all integers from 1 to 115): 6670 = 1+2+…+114+115.

 

6,671

[Geology]  The longest river in the world: Nile, in Egypt, 4145-mile or 6671-meter long.

 

6,680--6,689

[Math.] 

6680 = 6666+6+8+0

6681 = 6666+6+8+1

6682 = 6666+6+8+2

6683 = 6666+6+8+3

6684 = 6666+6+8+4

6685 = 6666+6+8+5

6686 = 6666+6+8+6

6687 = 6666+6+8+7

6688 = 6666+6+8+8

6689 = 6666+6+8+9.

 

6661, 6663, 6664, 6665, 6666, 6667, 6668 6669 and

6670, 6671, 6672, 6674 & 6675

[Math.]

66×64 = 4224

66×67 = 4422

66×68 = 4488

66×69 = 4554

66×74 = 4884

...

6666×6661 = 44402226

6666×6667 = 44442222

6666×6671 = 44468886

6666×6663 = 44415558

6666×6668 = 44448888

6666×6672 = 44475552

6666×6664 = 44422224

6666×6669 = 44455554

6666×6674 = 44488884

6666×6666 = 44435556

6666×6670 = 44462220

6666×6675 = 44495550

… (generalizable pattern) …