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600 | 601 | 602 | 603 | 604 | 605 | 606 | 607 | 608 | 609 |
610 | 611 | 612 | 613 | 614 | 615 | 616 | 617 | 618 | 619 |
620 | 621 | 622 | 623 | 624 | 625 | 626 | 627 | 628 | 629 |
630 | 631 | 632 | 633 | 634 | 635 | 636 | 637 | 638 | 639 |
640 | 641 | 642 | 643 | 644 | 645 | 646 | 647 | 648 | 649 |
650 | 651 | 652 | 653 | 654 | 655 | 656 | 657 | 658 | 659 |
660 | 661 | 662 | 663 | 664 | 665 | 666 | 667 | 668 | 669 |
670 | 671 | 672 | 673 | 674 | 675 | 676 | 677 | 678 | 679 |
680 | 681 | 682 | 683 | 684 | 685 | 686 | 687 | 688 | 689 |
690 | 691 | 692 | 693 | 694 | 695 | 696 | 697 | 698 | 699 |
The beast number or sign of the devil is equal to 666.[1] It is associated with Satan, evil, and bad luck in Western numerology.
The number's origin is in Revelation 13:18 from the Christian Bible: "This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666."[2] Some translations give 616.
A number with 666 digits is called an apocalypse number, and a number of the form 2n containing 666 in its decimal expansion is called an apocalyptic number.
Properties[]
Its prime factorization is 2 × 32 × 37.
A popular phenomenon in recreational mathematics is discovering "unusual" properties of 666 (purely coincidental). Here are some of them:
- 666 is the sum of the squares of the first seven primes: 22 + 32 + 52 + 72 + 112 + 132 + 172 = 666
- 666 = DCLXVI, using all of the Roman numerals except for M in descending order. For the same reason, the six Japanese yen coins sum to ¥666.
- φ(666) = 6 · 6 · 6, where φ represents Euler's totient function.
- 666 is the alternating sum of the first three sixth powers: 16 - 26 + 36.
- 666 is the 36th (6 · 6th) triangular number.
- 222,111 is the 666th triangular number, and the 222,111th triangular number is 24,666,759,216.
- There are exactly six digit 6's in the decimal expansion of 6666: 87,266,061,345,623,616.
- Similarly, there are 2 · 6 (12) digit 6's in the decimal expansion of 66666: 2,235,111,150,895,389,301,249,381,342,232,951,352,130,031,828,640,647,616,754,238,557,881,163,071,896,851,147,531,724,784,530,814,582,097,445,922,881,737,078,370,567,562,092,223,091,453,615,905,548,102,178,073,175,097,305,670,733,077,683,179,094,016.
- There are three ordered pandigital sums that produce 666, two increasing and one decreasing: 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21 = 666
- The first 144 (122) digits of pi add up to 666.
- The sine of the angle 666° multiplied by -2 is equal to the golden ratio.
- The sum of the first nine digits of pi in groups of three is: 314 + 159 + 265 = 666 + 66 + 6
- Similarly, if you reverse the digits, you get: 562 + 951 + 413 = 666 + 666 + 666 - 66 - 6
- Interestingly, by turning 666 upside down, you get 999, the UK official emergency number.
- The polar circles are at a latitude of around 66.6 degrees.
- It is also the prize for 4 correct final digits in the German lottery Super 6 in euros.
Sources[]
See also[]
- 777
- Legion's number of the first and second kind
- Leviathan number
- Super-leviathan
- Goliath number
Specific numbers: Beast number · Belphegor's prime · Legion's number of the first kind · Super-leviathan · Legion's number of the second kind · Leviathan number
Forms of numbers: apocalypse number · apocalyptic number · apocalyptri number · apocalyptetra number · apocalypenta number · apocalyhexakosioihexekontahexa number · Goliath number
beast number · twenty-twos · thirty-threes · forty-fours · fifty-fives · sixty-sixes · seventy-sevens · eighty-eights · ninety-nines