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We are nearly finished this Boinc project. There will be an article about our Euler project (included all known solutions up to N=250000) ! An interesting solution pair that caught my eyes: 170117^6+94978^6=154686^6+145994^6+97371^6+93828^6+61544^6 170117^6+144321^6=162972^6+138250^6+134979^6+106848...

New primitive solutions of the Euler(6,2,5) system: 237836^6+144025^6=193860^6+185703^6+18228^6+175588^6+201292^6 (Jrachi and EDGeS User) 232214^6+247261^6=192477^6+38682^6+9408^6+212492^6+249704^6 (sleeplift and cze_siek) 199096^6+127457^6=170244^6+147071^6+7462^6+147000^6+167412^6 (toms83 and Laur...

Has anyone else here noticed that the time to complete WU for Euler625 has nearly doubled lately? Only from around 1:15h to 2h (Q9450@3,2). To answer as the developer of the code: the workunits designed in such a way that it takes 4-8 GHz hours to complete a workunit. This is measured on Amd Athlon.

New primitive solutions from the previous ~3 weeks: 215993^6+87373^6=127608^6+1118^6+67438^6+88305^6+214389^6 (Bold_Seeker and Laurent Evrard) 237425^6+85667^6=233454^6+158280^6+68943^6+90685^6+103768^6 (ongekend41 and gow) 174745^6+74327^6=152574^6+141690^6+45864^6+81319^6+140329^6 (Laurent Evrard ...

New primitive solutions from the previous two weeks: 140915^6+4439^6=121836^6+53896^6+1925^6+100128^6+123375^6 (UL1 and wn1hgb) 135299^6+44033^6=86064^6+46820^6+2912^6+22743^6+133749^6 (Clay and Kristian_P) 186997^6+38987^6=46920^6+19018^6+140441^6+141057^6+173418^6 (tom and Laurent Evrard) 205201^6...

New primitive solutions: 187769^6+77335^6=159494^6+98688^6+91189^6+151683^6+155064^6 (Mumps [MM] and Laurent Evrard) 164117^6+106899^6=162396^6+86124^6+4725^6+58898^6+114387^6 (bachmann and Jrachi) 243781^6+4509^6=170532^6+111588^6+16107^6+76979^6+238308^6 (Laurent Evrard and Laurent Evrard) 205189^...

New primitive solutions from last two weeks: 220819^6+30665^6=98306^6+58818^6+86121^6+182672^6+206451^6 (Major and Cry) 158075^6+98173^6=78774^6+22054^6+69384^6+87255^6+158249^6 (mikkovi and [PNT] toms83) 209701^6+199073^6=143246^6+11130^6+168805^6+171780^6+211617^6 (mikkovi and Administrator and La...

Some notes to your estimate. First, we no need to check g = prime 4k+1, because in this case g² has only 2 decompositions to a sum of squares. So we can skip these diagonals. You are funny, when I make an estimation then in the next reply: no, you don't need to check some numbers and lower my origi...

For a more realictic view, we can ask even the next: How many odd numbers less than 2^64 has only 4k+1 primes in its decomposition to divisors, if the largest divisor is less than 2^32 (2^40 or any other number, that we will set as a goal) Why not simulate it? For 100000 random numbers gives 595 su...

You also haven't answered to my question that if you have a better bound or no than the known: g<=(X^2-1)/2. Because applying this if for example you could reach g<2^63, in this case you would prove the conjecture only for X<2^32 by a huge computation.

You still haven't answered to my questions. Let another example: g=18446744073709550105<2^64. For this g=5*13*p, where p>2^32. Where is the proof that this g can't be the space diagonal for a perfect Euler brick (I don't see). This example also shows that there are at least approx. primepi(2^64/5/13...

Now reading that message and your first post I see what you don't understand. What you want to do with Boinc is already known/searched... You want to search for g<2^32, where g is the space diagonal. But a^2+b^2+c^2=g^2, this means that (if X=odd term of {a,b,c}), X^2<g^2<2^64, so X<2^32. And this i...