Number 7 in Math

A page of the Numeropedia - the Special Encyclopedia of Numbers

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The largest 1-digit prime number.

The smallest odd prime number that is not a Fermat prime number.

Three numbers 3, 5 and 7 are the only three consecutive odd numbers, which are all prime numbers.

The 7th prime number is 17, sum of all prime numbers not greater than 7: 17 = 2+3+5+7.

A sequence of prime numbers: 9999907, 999907, 99907, 9907, 907 and 07.

The 4th Lucas number.

The regular 7-sided polygon (heptagon) is not constructible by using only straightedge and compass. The smallest such number.

The only independent number, which is not generated by any other number nor generates any other number between 2 and 10.

The 2nd Mersenne prime number: 23–1. It is the (1st) double Mersenne number. A Mersenne exponent: 27–1 = 127 is the 4th Mersenne prime number. Hence 127 is the (2nd) double Mersenne number.

Seven Bridges of Konigsberg”, a famous topology problem: to plan a continuous itinerary traveling over all 7 bridges of the city of Konigsberg (Germany) once and only once.

The minimum number of perfect riffle shuffles (when the deck is cut exactly in half and the cards are perfectly interlaced) to randomize a 52-card deck.

In general, the number of shuffles sufficient to randomize a large n-card deck is (1.5×log2n); i.e 9 shuffles are sufficient for a 52-card deck.

The smallest odd number that cannot be the difference of any 2 prime numbers.

The number of colors needed to paint a donut-shaped map to ensure that no adjacent areas/countries are of the same color.

Each ratio 16758/2394 = 18459/2637 = 31689/4527 = 36918/5274 = 37926/5418 = 41832/5976 = 53298/7614 = 7, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #7.

The two equalities 65821/9403 = 7 = 28651/4093 use all 10 digits 0-9 once in each equality.

74 = 2401 and 2+4+0+1 = 7.

The first Woodall prime number: 2×22–1 = 7. The first Woodall prime numbers (of the form n×2n–1) are with n = 2, 3, 6, 30, 75, 81…

The numerator of the 14th Bernoulli number: B14 = 7/6.

147 = 142–72 = (14+7)×7, where 14 = 7×2.

9513 = 1359×7.

27,594 = 7×3942 = 73×9×42.

510,510 is the product of first 7 prime numbers, of 2 consecutive numbers and of 4 consecutive Fibonacci numbers:

510,510 = 2×3×5×7×11×13×17 = 714×715 = 13×21×34×55.

6×7×9×524×831 = 164,597,832, using each of 9 digits 1-9 once on both sides of the equality.

The equality 9304×7 = 65,128 uses each of 10 digits 0-9 once.

1×7 + 3 = 10

14×7 + 2 = 100

142×7 + 6 = 1000

1428×7 + 4 = 10000

14285×7 + 5 = 100000

142857×7 + 1 = 1000000

1428571×7 + 3 = 10000000

14285714×7 + 2 = 100000000

142857142×7 + 6 = 1000000000

1428571428×7 + 4 = 10000000000

14285714285×7 + 5 = 100000000000

142857142857×7 + 1 = 1000000000000

1428571428571×7 + 3 = 10000000000000

7,101,449,275,362,318,840,579 = 1,014,492,753,623,188,405,797×7.

Two 7-pseudoparasite numbers:

7,101,449,275,362,318,840,579 = 1,014,492,753,623,188,405,797×7.

9,130,434,782,608,695,652,173 = 1,304,347,826,086,956,521,739×7.

Sum of all prime numbers from 7 to 53 is the product of 2 numbers themselves, 7 and 53:

371 = 7×53 = 7+11+13+17+19+23+29+31+37+41+43+47+53.

1/7 = 0.142857142857… or 0.142857. Multiples of 142857 by 2, 3, 4, 5 and 6 yield 5 other rotations of the digits of the number itself: 285714, 428571, 571428, 714285 and 857142, respectively. Its multiple by 7 is 999999.

The number of colors sufficient to color any map on a torus such that no pair of adjacent regions has the same color.

Seven circles theorem: Given a circle, draw 6 circles (not necessary the same size, either outside or inside the original circle or both) tangent two neighbor circles and the original circle. The 3 lines joining points of contact of opposite pairs of circles with the original circle are concurrent.

The Fermat quotient (2p –1–1)/p is a square number only when p = 3 and 7.

The product of the first 8 consecutive prime numbers, divided by 10:  2×3×5×7×11×13×17×19/10 = 969,969 is a palindromic number.

3,122,490 = 2×3×5×7×14869, whose prime factors use each of 9 digits 1-9 once.