This page contains lottery-related numbers.

## Edit

### 5/n lotteries Edit

In Pennsylvania, there is a 5/30 lottery called *Treasure Hunt*, where you must pick 5 numbers out of 30. Therefore, the number of possible combinations is equal to _{30}C_{5} = **142,506**.

Its prime factorization is 2 × 3^{3} × 7 × 13 × 29.

In Virginia, there is a 5/34 lottery called *Cash 5*, where you must pick 5 numbers out of 34. Therefore, the number of possible combinations is equal to _{34}C_{5} = **278,256**.

Its prime factorization is 2^{4} × 3 × 11 × 17 × 31.

In Russia, there is a 5/36 lottery, where you must pick 5 numbers out of 36. Therefore, the number of possible combinations is equal to _{36}C_{5} = **376,992**.

Its prime factorization is 2^{5} × 3^{2} × 7 × 11 × 17.

In New York, there is a 5/39 lottery called *Take 5*, where you must pick 5 numbers out of 39. Therefore, the number of possible combinations is equal to _{39}C_{5} = **575,757**.

Its prime factorization is 3^{2} × 7 × 13 × 19 × 37.

In Iceland, there is a 5/40 lottery, where you must pick 5 numbers out of 40. Therefore, the number of possible combinations is equal to _{40}C_{5} = **658,008**.

Its prime factorization is 2^{3} × 3^{2} × 13 × 19 × 37.

In North Carolina, there is a 5/41 lottery called *Carolina Cash 5*, where you must pick 5 numbers out of 41. Therefore, the number of possible combinations is equal to _{41}C_{5} = **749,398**.

Its prime factorization is 2 × 13 × 19 × 37 × 41.

In the U.S. state of Georgia, there is a 5/42 lottery called *Fantasy 5*, where you must pick 5 numbers out of 42. Therefore, the number of possible combinations is equal to _{42}C_{5} = **850,668**.

Its prime factorization is 2^{2} × 3 × 7 × 13 × 19 × 41.

In Pennsylvania, there is a 5/43 lottery called *Cash 5*, where you must pick 5 numbers out of 43. Therefore, the number of possible combinations is equal to _{43}C_{5} = **962,598**.

Its prime factorization is 2 × 3 × 7 × 13 × 41 × 43.

In Ukraine, there is a 5/45 lottery, where you must pick 5 numbers out of 45. Therefore, the number of possible combinations is equal to _{45}C_{5} = **1,221,759**.

Its prime factorization is 3^{2} × 7 × 11 × 41 × 43.

In Uruguay, there is a 5/48 lottery, where you must pick 5 numbers out of 48. Therefore, the number of possible combinations is equal to _{48}C_{5} = **1,712,304**.

Its prime factorization is 2^{4} × 3^{2} × 11 × 23 × 47.

In the card game of poker, a poker hand can be any combination of 5 cards of a standard 52-card deck. Therefore, the number of possible combinations is equal to _{52}C_{5} = **2,598,960**.

In some U.S. states, such as Arizona, Indiana and Kentucky, there is a 5/52 lottery, where you must pick 5 cards out of 52, or they are generated by a terminal.

Its prime factorization is 2^{4} × 3 × 5 × 7^{2} × 13 × 17.

In some countries, such as Italy, there is a 5/90 lottery, where you must pick 5 numbers out of 90. The number of possible combinations is equal to _{90}C_{5} = **43,949,268**.

Its prime factorization is 2^{2} × 3^{2} × 11 × 29 × 43 × 89.

### 6/n lotteries Edit

In the country of Georgia, there is a 6/36 lottery, where you must pick 6 numbers out of 36. Therefore, the number of possible combinations is equal to _{36}C_{6} = **1,947,792**.

Its prime factorization is 2^{4} × 3 × 7 × 11 × 17 × 31.

In New Zealand, there is a 6/40 lottery called *Lotto*, where you must pick 6 numbers out of 40. Therefore, the number of possible combinations is equal to _{40}C_{6} = **3,838,380**.

Its prime factorization is 2^{2} × 3 × 5 × 7 × 13 × 19 × 37.

In the Philippines, there is a 6/42 lottery, where you must pick 6 numbers out of 42. Therefore, the number of possible combinations is equal to _{42}C_{6} = **5,245,786**.

Its prime factorization is 2 × 7 × 13 × 19 × 37 × 41.

In Japan, there is a 6/43 lottery, where you must pick 6 numbers out of 43. Therefore, the number of possible combinations is equal to _{43}C_{6} = **6,096,454**.

Its prime factorization is 2 × 7 × 13 × 19 × 41 × 43.

In some countries, such as the Netherlands, there is a 6/45 lottery, where you must pick 6 numbers out of 45. The number of possible combinations is equal to _{45}C_{6} = **8,145,060**.

Its prime factorization is 2^{2} × 3 × 5 × 7 × 11 × 41 × 43.

In the Republic of Ireland, there is a 6/47 lottery, where you must pick 6 numbers out of 47. Therefore, the number of possible combinations is equal to _{47}C_{6} = **10,737,573**.

Its prime factorization is 3 × 7 × 11 × 23 × 43 × 47.

In some countries, such as Germany, there is a 6/49 lottery, where you must pick 6 numbers out of 49. The number of possible combinations is equal to _{49}C_{6} = **13,983,816**.

Its prime factorization is 2^{3} × 3 × 7^{2} × 11 × 23 × 47.

In some countries, such as South Africa and Ukraine, there is a 6/52 lottery, where you must pick 6 numbers out of 52. Therefore, the number of possible combinations is equal to _{52}C_{6} = **20,358,520**.

Its prime factorization is 2^{3} × 5 × 7^{2} × 13 × 17 × 47.

In Florida, there is a 6/53 lottery called *Florida Lotto*, where you must pick 6 numbers out of 53. Therefore, the number of possible combinations is equal to _{53}C_{6} = **22,957,480**.

Its prime factorization is 2^{3} × 5 × 7^{2} × 13 × 17 × 53.

In Texas, there is a 6/54 lottery called *Lotto Texas*, where you must pick 6 numbers out of 54. Therefore, the number of possible combinations is equal to _{54}C_{6} = **25,827,165**.

Its prime factorization is 3^{2} × 5 × 7^{2} × 13 × 17 × 53.

In the Philippines, there is a 6/55 lottery, where you must pick 6 numbers out of 55. Therefore, the number of possible combinations is equal to _{55}C_{6} = **28,989,675**.

Its prime factorization is 3^{2} × 5^{2} × 11 × 13 × 17 × 53.

In Mexico, there is a 6/56 lottery, where you must pick 6 numbers out of 56. Therefore, the number of possible combinations is equal to _{56}C_{6} = **32,468,436**.

Its prime factorization is 2^{2} × 3^{2} × 7 × 11 × 13 × 17 × 53.

In the Philippines, there is a 6/58 lottery, where you must pick 6 numbers out of 58. Therefore, the number of possible combinations is equal to _{58}C_{6} = **40,475,358**.

Its prime factorization is 2 × 3^{2} × 7 × 11 × 19 × 29 × 53.

In the United Kingdom, there is a 6/59 lottery, where you must pick 6 numbers out of 59. The number of possible combinations is equal to _{59}C_{6} = **45,057,474**.

Its prime factorization is 2 × 3^{2} × 7 × 11 × 19 × 29 × 59.

In Brazil, there is a 6/60 lottery called *Mega-Sena*, where you must pick 6 numbers out of 60. Therefore, the number of possible combinations is equal to _{60}C_{6} = **50,063,860**.

Its prime factorization is 2^{2} × 5 × 7 × 11 × 19 × 29 × 59.

In Italy, there is a 6/90 lottery, where you must pick 6 numbers out of 90. The number of possible combinations is equal to _{90}C_{6} = **622,614,630**.

Its prime factorization is 2 × 3 × 5 × 11 × 17 × 29 × 43 × 89.

### 7/n lotteries Edit

In Norway, there is a 7/34 lottery, where you must pick 7 numbers out of 34. The number of possible combinations is equal to _{34}C_{7} = **5,379,616**.

Its prime factorization is 2^{5} × 11 × 17 × 29 × 31.

In Sweden, there is a 7/35 lottery, where you must pick 7 numbers out of 35. The number of possible combinations is equal to _{35}C_{7} = **6,724,520**.

Its prime factorization is 2^{3} × 5 × 11 × 17 × 29 × 31.

In Denmark, there is a 7/36 lottery, where you must pick 7 numbers out of 36. The number of possible combinations is equal to _{36}C_{7} = **8,347,680**.

Its prime factorization is 2^{5} × 3^{2} × 5 × 11 × 17 × 31.

In some countries, such as Finland, Serbia and Slovenia, there is a 7/39 lottery, where you must pick 7 numbers out of 39. The number of possible combinations is equal to _{39}C_{7} = **15,380,937**.

Its prime factorization is 3^{2} × 11 × 13 × 17 × 19 × 37.

In Australia, there is a 7/45 lottery called *Oz Lotto*, where you must pick 7 numbers out of 45. Therefore, the number of possible combinations is equal to _{45}C_{7} = **45,379,620**.

Its prime factorization is 2^{2} × 3^{2} × 5 × 11 × 13 × 41 × 43.

In Canada, there is a 7/49 lottery called *Lotto Max*, where you must pick 7 numbers out of 49. Therefore, the number of possible combinations is equal to _{49}C_{7} = **85,900,584**.

Its prime factorization is 2^{3} × 3 × 7 × 11 × 23 × 43 × 47.

### Other single-drum lotteries Edit

In the U.S. state of Washington, there is a 4/24 lottery called *Match 4*, where you must pick 4 numbers out of 24. Therefore, the number of possible combinations is equal to _{24}C_{4} = **10,626**.

Its prime factorization is 2 × 3 × 7 × 11 × 23.

In New Zealand, there is a 4/40 lottery called *Lotto Strike*, where you must pick 4 numbers out of 40 in the correct order. Therefore, the number of possible combinations is equal to _{40}P_{4} = **2,193,360**.

Its prime factorization is 2^{4} × 3 × 5 × 13 × 19 × 37.

In parts of the United States, there is a 12/24 lottery called *All or Nothing*, where you must pick 12 numbers out of 24. Therefore, the number of possible combinations is equal to _{24}C_{12} = **2,704,156**.

Its prime factorization is 2^{2} × 7 × 13 × 17 × 19 × 23.

In Venezuela, there is a 15/25 lottery, where you must pick 15 numbers out of 25. Therefore, the number of possible combinations is equal to _{25}C_{15} = **3,268,760**.

Its prime factorization is 2^{3} × 5 × 11 × 17 × 19 × 23.

In the Czech republic, there is a lottery named Šťastných 10 (literally "Happy 10"), where you pick 1-10 numbers of 80. When it draws, 20 numbers of 80 numbers are drawn. The number of possible combination of the drawing is _{80}C_{20} = **3,535,316,142,212,174,320** (3 and a half quintillion combinations in short scale, or 3 and a half trillion combinations in long scale).^{[1]}

The table of chances is given below: (The table is written in Czech Koruna, where 1£ ~ 28 Kč and 1$ ~ 22 Kč)

Number of judged combinations | ✖ | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |

10 | 200,000× | ||||||||||

9 | 10,000× | 50,000× | |||||||||

8 | 500× | 2,000× | 20,000× | ||||||||

7 | 20× | 200× | 400× | 4,000× | |||||||

6 | 10× | 20× | 40× | 100× | 600× | ||||||

5 | 3× | 3× | 4× | 10× | 20× | 200× | |||||

4 | Nothing | Nothing | 1× | 2× | 2× | 16× | 50× | ||||

3 | Nothing | Nothing | Nothing | Nothing | 1× | 2× | 8× | 16× | |||

2 | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | 2× | 8× | ||

1 | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | 2× | |

0 | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing | Nothing |

Its prime factorization is 2^{4} × 5 × 7 × 11 × 13 × 23 × 31 × 37 × 61 × 67 × 71 × 73 × 79.

In parts of Australia, there is a 4/45 lottery called *Lotto Strike*, where you must pick 4 numbers out of 45 in the correct order. Therefore, the number of possible combinations is equal to _{45}P_{4} = **3,575,880**.

Its prime factorization is 2^{3} × 3^{3} × 5 × 7 × 11 × 43.

In Australia, there is a 8/37 lottery called *Set For Life*, where you must pick 8 numbers out of 37. Therefore, the number of possible combinations is equal to _{37}C_{8} = **38,608,020**.

Its prime factorization is 2^{2} × 3^{2} × 5 × 11 × 17 × 31 × 37.

In Chile, there is a 14/25 lottery, where you must pick 14 numbers out of 25. Therefore, the number of possible combinations is equal to _{25}C_{14} = **4,457,400**.

Its prime factorization is 2^{3} × 3 × 5^{2} × 17 × 19 × 23.

### Mega Ball lotteries Edit

In Canada, there is a 5/49+1/7 lottery called *Daily Grand*, where you must pick 5 numbers out of 49, and 1 number out of 7. Therefore, the number of possible combinations is equal to _{5}C_{49} × 7 = **13,348,188**.

Its prime factorization is 2^{2} × 3^{2} × 7^{3} × 23 × 47.

In Germany, there is a 6/49+1/10 lottery, where you must pick 6 numbers out of 49, and the final digit of the serial number is used for determining the top prize. Therefore, the number of possible combinations is _{49}C_{6} × 10.

In some other Western European countries, there is a 5/50+2/12 lottery called *EuroMillions*, where you must pick 5 numbers out of 50, and 2 numbers out of 12. Therefore, the number of possible combinations is _{50}C_{5} × _{12}C_{2}.

Both _{49}C_{6} × 10 and _{50}C_{5} × _{12}C_{2} are equal to **139,838,160**.

Its prime factorization is 2^{4} × 3 × 5 × 7^{2} × 11 × 23 × 47.

In Colombia, there is a 5/43+1/16 lottery, where you must pick 5 numbers out of 43, and 1 number out of 16. Therefore, the number of possible combinations is equal to _{43}C_{5} × 16 = **15,401,568**.

Its prime factorization is 2^{5} × 3 × 7 × 13 × 41 × 43.

In Israel, there is a 6/37 + 1/7 lottery, where you must pick 6 numbers out of 37, and 1 number out of 7. The number of possible combinations is equal to _{37}C_{6} × 7 = **16,273,488**.

Its prime factorization is 2^{4} × 3 × 7^{2} × 11 × 17 × 37.

In France, there is a 5/49+1/10 lottery, where you must pick 5 numbers out of 49, and 1 number out of 10. Therefore, the number of possible combinations is equal to _{5}C_{49} × 10 = **19,068,840**.

Its prime factorization is 2^{3} × 3^{2} × 5 × 7^{2} × 23 × 47.

In parts of the United States, there is a 5/60+1/4 lottery called *Cash4Life*, where you must pick 5 numbers out of 60, and 1 number out of 4. Therefore, the number of possible combinations is equal to _{60}C_{5} × 4 = **21,846,048**.

Its prime factorization is 2^{5} × 3 × 7 × 19 × 29 × 59.

In Argentina, there is a 6/42+2/10 lottery, where you must pick 6 numbers out of 42, and 2 numbers out of 10. Therefore, the number of possible combinations is equal to _{42}C_{6} × _{10}C_{2} = **236,060,370**.

Its prime factorization is 2 × 3^{2} × 5 × 7 × 13 × 19 × 37 × 41.

In South Africa, there is a 5/45 + 1/20 lottery, where you must pick 5 numbers out of 45, and 1 number out of 20. Therefore, the number of possible combinations is equal to _{45}C_{5} × 20 = **24,435,180**.

Its prime factorization is 2^{2} × 3^{2} × 5 × 7 × 11 × 41 × 43.

In Portugal, there is a 5/49+1/13 lottery, where you must pick 5 numbers out of 49, and 1 number out of 13. Therefore, the number of possible combinations is equal to _{5}C_{49} × 13 = **24,789,492**.

Its prime factorization is 2^{2} × 3^{2} × 7^{2} × 13 × 23 × 47.

In the United States, there is a 5/75+1/15 lottery called *Mega Millions*, where you must pick 5 numbers out of 75, and 1 number out of 15. Therefore, the number of possible combinations is equal to _{75}C_{5} × 15 = **258,890,850**.

Its prime factorization is 2 × 3^{3} × 5^{2} × 37 × 71 × 73.

In parts of the United States, there is a 5/47+1/19 lottery called *Hot Lotto*, where you must pick 5 numbers out of 47, and 1 number out of 19. Therefore, the number of possible combinations is equal to _{47}C_{5} × 19 = **29,144,841**.

Its prime factorization is 3 × 11 × 19 × 23 × 43 × 47.

In the United States, there is a 5/69+1/26 lottery called *Powerball*, where you must pick 5 numbers out of 69, and 1 number out of 26. Therefore, the number of possible combinations is equal to _{69}C_{5} × 26 = **292,201,338**.

Its prime factorization is 2 × 3 × 11 × 13^{2} × 17 × 23 × 67.

In Croatia, there is a 7/39 + 1/2 lottery, where you must pick 7 numbers out of 39, and 1 letter out of 2. The number of possible combinations is equal to _{39}C_{7} × 2 = **30,761,874**.

Its prime factorization is 2 × 3^{2} × 11 × 13 × 17 × 19 × 37.

In parts of the United States, there is a 5/48+1/18 lottery called *Lucky for Life*, where you must pick 5 numbers out of 48, and 1 number out of 18. Therefore, the number of possible combinations is equal to _{48}C_{5} × 18 = **30,821,472**.

Its prime factorization is 2^{5} × 3^{4} × 11 × 23 × 47.

In Switzerland, there is a 6/42 + 1/6 lottery, where you must pick 6 numbers out of 42, and 1 number out of 6. The number of possible combinations is equal to _{42}C_{6} × 6 = **31,474,716**.

Its prime factorization is 2^{2} × 3 × 7 × 13 × 19 × 37 × 41.

In Spain, there is a 5/54+1/10 lottery called *El Gordo de la Primitiva*, where you must pick 5 numbers out of 54, and 1 number out of 10. Therefore, the number of possible combinations is equal to _{54}C_{5} × 10 = **31,625,100**.

Its prime factorization is 2^{2} × 3^{3} × 5^{2} × 13 × 17 × 53.

In New Zealand, there is a 6/40+1/10 lottery called *Powerball*, where you must pick 6 numbers out of 40, and 1 number out of 10. Therefore, the number of possible combinations is equal to _{40}C_{6} × 10 = **38,383,800**.

Its prime factorization is 2^{3} × 3 × 5^{2} × 7 × 13 × 19 × 37.

In California, there is a 5/47+1/27 lottery called *SuperLotto Plus*, where you must pick 5 numbers out of 47, and 1 number out of 27. Therefore, the number of possible combinations is equal to _{47}C_{5} × 27 = **41,416,353**.

Its prime factorization is 3^{4} × 11 × 23 × 43 × 47.

In the Netherlands, there is a 6/45 + 1/6 lottery, where you must pick 6 numbers out of 45, and 1 color out of 6. The number of possible combinations is equal to _{45}C_{6} × 6 = **48,870,360**.

Its prime factorization is 2^{3} × 3^{2} × 5 × 7 × 11 × 41 × 43.

In Chile, there is a 7/30+1/3 lottery, where you must pick 7 numbers out of 30, and 1 number out of 3. Therefore, the number of possible combinations is equal to _{30}C_{7} × 3 = **6,107,400**.

Its prime factorization is 2^{3} × 3^{4} × 5^{2} × 13 × 29.

In Australia, there is a 6/40+1/20 lottery called *Powerball*, where you must pick 6 numbers out of 40, and 1 number out of 20. Therefore, the number of possible combinations is equal to _{40}C_{6} × 20 = **76,767,600**.

Its prime factorization is 2^{4} × 3 × 5^{2} × 7 × 13 × 19 × 37.

In the United Kingdom, there is a 5/39+1/14 lottery called *Thunderball*, where you must pick 5 numbers out of 39, and 1 number out of 14. Therefore, the number of possible combinations is equal to _{39}C_{14} × 10 = **8,060,598**.

Its prime factorization is 2 × 3^{2} × 7^{2} × 13 × 19 × 37.

#### Expressions in other bases Edit

- In hexadecimal, 7A FEB6
- In binary, 111 1010 1111 1110 1011 0110

#### Approximations Edit

Notation | Approximation |
---|---|

Scientific notation | \(8.0606*10^{6}\) |

Arrow notation | \(2,839↑ 2<n<2,840↑ 2\) |

Chained arrow notation | \(2,839→ 2<n<2,840→ 2\) |

BEAF | \(\{2839,2\}\) |

Hyperfactorial array notation | \(10!\) |

Fast-growing hierarchy | \(f_2(19)\) |

Hardy hierarchy | \(H_{\omega^2}(19)\) |

Slow-growing hierarchy | \(g_{\omega^2}(2,839)\) |

In Germany and some other European countries, there is a 5/50+2/10 lottery called *Eurojackpot*, where you must pick 5 numbers out of 50, and 2 numbers out of 10. Therefore, the number of possible combinations is equal to _{50}C_{5} × _{10}C_{2} = **95,344,200**.

Its prime factorization is 2^{3} × 3^{2} × 5^{2} × 7^{2} × 23 × 47.

In Northern Europe, there is a 6/48+1/8 lottery called *Viking Lotto*, where you must pick 6 numbers out of 48, and 1 number out of 8. Therefore, the number of possible combinations is equal to _{48}C_{6} × 8 = **98,172,096**.

Its prime factorization is 2^{6} × 3 × 11 × 23 × 43 × 47.

### Other multi-drum lotteries Edit

In Slovenia, there is a (3/8)*3 lottery, where you must pick three fields with 3 numbers out of 8. Therefore, the number of possible combinations is equal to (_{8}C_{3})^{3} = **175,616**.

Its prime factorization is 2^{9} × 7^{3}.

In Russia, there is a (4/20)*2 lottery, where you must pick two fields with 4 numbers out of 20. Therefore, the number of possible combinations is equal to (_{20}C_{4})^{2} = **23,474,025**.

Its prime factorization is 3^{2} × 5^{2} × 17^{2} × 19^{2}.

### Sources Edit

- ↑ Šťastných 10 – pravidla, šance na výhru (in Czech)