33 = (8,866,128,975,287,528)³ + (-8,778,405,442,862,239)³ + (-2,736,111,468,807,040)³

[retina]

Bristol mathematician cracks Diophantine puzzle

33 = (8,866,128,975,287,528)³ + (-8,778,405,442,862,239)³ + (-2,736,111,468,807,040)³

The next and final unsolved number under 100 – 42 – has the appeal of being Douglas Adams' answer to the meaning of life. Dr. Booker is currently working with Andrew Sutherland from MIT to find it.

[henryzz]

The relevant numberphile video:
https://www.youtube.com/watch?v=ASoz_NuIvP0

[retina]

Originally Posted by henryzz

The relevant numberphile video:
https://www.youtube.com/watch?v=ASoz_NuIvP0

That guy is really cool.

[bsquared]

Originally Posted by retina

That guy is really cool.

He's also on this forum - Congrats arbooker! Looking forward to seeing 42 cracked

[Nick]

Details: https://people.maths.bris.ac.uk/~maa...456.1554223010

[Stargate38]

If anyone wants to know, here are the factorizations:

8866128975287528=2^3*7*467*378289*896201
8778405442862239=8778405442862239
2736111468807040=2^7*5*89917*47545783

[Batalov]

Originally Posted by Stargate38

If anyone wants to know, here are the factorizations:

8866128975287528=2^3*7*467*378289*896201
8778405442862239=8778405442862239
2736111468807040=2^7*5*89917*47545783

[retina]

Originally Posted by bsquared

He's also on this forum - Congrats arbooker! Looking forward to seeing 42 cracked

Professors Booker and Sutherland's solution for 42 would be found by using Charity Engine; a 'worldwide computer' that harnesses idle, unused computing power from over 500,000 home PCs to create a crowd-sourced, super-green platform made entirely from otherwise wasted capacity.

The answer, which took over a million hours of calculating to prove

42 = (-80538738812075974)³ + (80435758145817515)³ + (12602123297335631)³

[rudy235]

Booker says in the Video that (Minute 12:35) Heath Brown calculated that for this small numbers i.e ≤ 100. You would expect "the numbers from one solution to the next to increase by a factor of millions".
https://www.youtube.com/watch?v=ASoz_NuIvP0


Yet the numbers have increased only by one order of magnitude. (10)

So the question is this. Is this a completely off the chart finding? or are Heath Brown Calculations off base?

Video of "42" https://www.youtube.com/watch?v=zyG8Vlw5aAw

[retina]

Originally Posted by rudy235

So the question is this. Is this a completely off the chart finding? or are Heath Brown Calculations off base?

Yes. Or no. We don't know. One data point isn't going to tell you much of value here.

[rudy235]

Originally Posted by retina

Yes. Or no. We don't know. One data point isn't going to tell you much of value here.

That is a good answer, but it is also sort of an

e-a-s-y answer.

We all know full well that one point is not enough to make good conclusions, we can agree on that, but... very early on in the sixties (60's) they went over 20 fold and did not find a new solution. And because of this, Heath Brown tried to figure what would happen along the line and concluded that 20-fold was not enough. He postulated a million-fold.

Now, he might be wrong, but if I were a betting man I would say he did as good analysis on the matter as could have been done at the time, and concluded that the sparsity was so intense that a 20-fold increase in the search would not normally produce a new result.

In other words, with the evidence we have as such, I am inclined to think this result for 42 is indeed an extraordinary and lucky result.

Of course, I may be totally wrong, but that is my feeling. (At least for now)