The extremely weird 'Number 47' phenomenon is best experienced through the unique insight of a group of experts who call themselves the '47 Society'. I strongly recommend their website for exhaustive information on this bizarre number... Here is its official description:

What is the 47 Society?

The 47 Society is an international interest-group that follows the occurence and recurrence of the quintessential random number: 47. Many suspect that the coinciential nature of 47 carries some mystical, metaphysical and/or scientific significance. The phenomenon may have first been documented at Pomona College in 1964, when Professor Donald Bentley proved that all numbers are equal to 47. Coincidentally, 47 seems to occur on or near the college campus with amazing frquency, even by enthusiast standards. But make no mistake: 47 is everywhere and people were noticing it long before 1964. The 47 Society Web Site is the global source for 47 information.

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There are quite a few other notable '47'-based websites, not the least of wich is the famous 'Land of Schlock' where you will find unique '47'-resources, including a comprehensive list of '47' occurences in Star Trek, as well as the scanned image of a personal letter from Star Trek writer Brannon Braga to Miss Shlock (the site author) concerning her brilliant treatment of the '47' case...!
Or you can visit the
Pomona College website, which seems to be part of the origin of the legend...

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And for the sceptical, here is an appetizer-sized list of examples of Number 47's recurrent appearances in Star Trek episodes...

The Next Generation:

"I, Borg" The invasion program is labeled "topological anomaly 4747"

"Relics" Scotty is 147 years old

"A Fistful of Datas" The affected computer system is subroutine C-47

"Descent" Steven Hawking wins the poker round with four sevens

"All Good Things..." Riker is the CO of Starbase 247

Deep Space Nine

"Playing God" At one point, Dax changes course to "130 mark 47

"Defiant" Kira's access code is delta 5-4-7

"Shakaar" O"Brien is poised to win his 47th dart game in a row

"The Visitor" Jake writes on a PADD with the number 4747 in the upper left-hand corner

"Return to Grace" The time for the first battle drilll on Dukat's ship is: "three forty-seven"

Voyager

"Caretaker" The energy pulses increase by "point four seven" seconds in frequency

"Emanations" The crew discovers the 247th element

"Elogium" Shields at one point are at 47 percent

"Prototype" B'Elanna reactivates Automated Personnel Unit 3947

"Lifesigns" Since his activation, the Doctor says he has performed 347 medical exams

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