13532385396179 - Numberphile
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Date: 2022-04-08
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Comments and reviews: 9
Rick
The choice of example at 2: 00 is a little unfortunate. 2-2-3-5 becomes 2235, but it's not obvious whether the second digit is 2 because that's the exponent of the first 2, or because that factor is repeated in the factorization (60 = 2-2-3-5. At first I thought it was the latter (which somehow feels more natural: why should the exponent be treated the same way as one of the factors, in which case Davis's example obviously isn't correct.
I'm now curious about the conjecture as it applies to my alternate formulation, in which e. g. 30 would climb to 2555 (2-5-5-5. Perhaps -that- always ends on a prime. No reward from me, though!
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The choice of example at 2: 00 is a little unfortunate. 2-2-3-5 becomes 2235, but it's not obvious whether the second digit is 2 because that's the exponent of the first 2, or because that factor is repeated in the factorization (60 = 2-2-3-5. At first I thought it was the latter (which somehow feels more natural: why should the exponent be treated the same way as one of the factors, in which case Davis's example obviously isn't correct.
I'm now curious about the conjecture as it applies to my alternate formulation, in which e. g. 30 would climb to 2555 (2-5-5-5. Perhaps -that- always ends on a prime. No reward from me, though!
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Olaf
Can Tony Padilla do an extra bit of explanation?
Reading the video paused at 4: 38 (read the lower part before the upper part of the text) I still don't understand how to find m=1407 to generate this number as 140700001x96179. I get, that 00001 is just there to let 96179 be concatenated to 1407x96179=135323853, so I get why you construct x=m-10-y+1as a number ending in y-1 zero digits and a final 1 digit, but I don't get, why that forces the prime factorization so 13532385396179 climbs to itself. I don't get why the part 135323853 results in the other prime factors 13x53-2x3853.
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Can Tony Padilla do an extra bit of explanation?
Reading the video paused at 4: 38 (read the lower part before the upper part of the text) I still don't understand how to find m=1407 to generate this number as 140700001x96179. I get, that 00001 is just there to let 96179 be concatenated to 1407x96179=135323853, so I get why you construct x=m-10-y+1as a number ending in y-1 zero digits and a final 1 digit, but I don't get, why that forces the prime factorization so 13532385396179 climbs to itself. I don't get why the part 135323853 results in the other prime factors 13x53-2x3853.
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Miko
Hi, I was hoping somebody watching this video or -Numberphile could help me
After a short while Google searching I have been able to find exceedingly little on these 5 problems of John Conway's; I have found two identical versions of the pdf stating the problems but no discussion of them online whatsoever - I was wondering, which of these have been proved thus far, and by extension which of the problem remain to be solved? Evidently Problem 5 has been answered, but have any of the others?
Thanks for taking the time to read this =)
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Hi, I was hoping somebody watching this video or -Numberphile could help me
After a short while Google searching I have been able to find exceedingly little on these 5 problems of John Conway's; I have found two identical versions of the pdf stating the problems but no discussion of them online whatsoever - I was wondering, which of these have been proved thus far, and by extension which of the problem remain to be solved? Evidently Problem 5 has been answered, but have any of the others?
Thanks for taking the time to read this =)
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Edo
13-53-53-3853=140700001, so checking if multiplying this with 96179 actually equals 13532385396179 can easily be done on a 10 digit calculator: when you multiply 1407 with 96179 you get 135323853, the first 9 digits of the total product. Then check if the final 5 digits in the total product are 96179 and indeed they are. Makes me wonder if this is a coincidence or if this fact was used in finding 13532385396179 as an example.
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13-53-53-3853=140700001, so checking if multiplying this with 96179 actually equals 13532385396179 can easily be done on a 10 digit calculator: when you multiply 1407 with 96179 you get 135323853, the first 9 digits of the total product. Then check if the final 5 digits in the total product are 96179 and indeed they are. Makes me wonder if this is a coincidence or if this fact was used in finding 13532385396179 as an example.
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lostindixie
Question about these kinds of numerical properties - are they properties of the quantity itself or the way the quantity is expressed in base ten? If the former it is a mathematical truth, if the latter it is a parlor trick.
I have tried taking the binary and hexidecimal equivalents of 13532385396179 to see if the same can be done with the value expressed in a different base. So far, it doesn't seem to hold.
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Question about these kinds of numerical properties - are they properties of the quantity itself or the way the quantity is expressed in base ten? If the former it is a mathematical truth, if the latter it is a parlor trick.
I have tried taking the binary and hexidecimal equivalents of 13532385396179 to see if the same can be done with the value expressed in a different base. So far, it doesn't seem to hold.
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education
The first thing I thought of when I saw this was how to me, it seems that something like 5-2 --> 52 seems somewhat arbitrary and shorthand, while 5-5 --> 55 feels more -correct- or natural. I'm not even sure what I'm trying to get at, but I guess it just makes me wonder what the deeper implications are. What's -under the hood- so to speak. Anyone else feel this way?
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The first thing I thought of when I saw this was how to me, it seems that something like 5-2 --> 52 seems somewhat arbitrary and shorthand, while 5-5 --> 55 feels more -correct- or natural. I'm not even sure what I'm trying to get at, but I guess it just makes me wonder what the deeper implications are. What's -under the hood- so to speak. Anyone else feel this way?
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education
The first thing I thought of when I saw this was how, to me it seems that 5-2 --> 52 seems somewhat arbitrary and shorthand, while 5-5 --> 55 feels more -correct- or natural. I'm not even sure what I'm trying to get at, but I guess it just makes me wonder what the deeper implications are. What's -under the hood- so to speak. Anyone else feel this way?
reply
The first thing I thought of when I saw this was how, to me it seems that 5-2 --> 52 seems somewhat arbitrary and shorthand, while 5-5 --> 55 feels more -correct- or natural. I'm not even sure what I'm trying to get at, but I guess it just makes me wonder what the deeper implications are. What's -under the hood- so to speak. Anyone else feel this way?
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Chounoki
If you try out every number and set out a reasonable max step in computer, then let it run for months, you should be able to find a counter example if there are some. I guess that could be how he found it. But I reckon ordinary people just wouldn't bother to do it.
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If you try out every number and set out a reasonable max step in computer, then let it run for months, you should be able to find a counter example if there are some. I guess that could be how he found it. But I reckon ordinary people just wouldn't bother to do it.
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00Billy
Thought I remember a video about the univsersal constants. lots on planck.
one thing I remember is Pi to 14 digits is all you need given.
does that apply to the other constants too then?
Anyone know a pi estimation that handles 15 digits?
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Thought I remember a video about the univsersal constants. lots on planck.
one thing I remember is Pi to 14 digits is all you need given.
does that apply to the other constants too then?
Anyone know a pi estimation that handles 15 digits?
reply
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