Welcome to Uwe's occasionally-updated web page about Ramanujan numbers. If you'd like to contact me, you can send email to me at uhollerbach@gmail.com.
Here are all the files related to Ramanujan numbers:
mod 100 (about 28 MB)1 + A3, ie, those for which
A^3 is almost equal to
B3 + C3: Fermat near-misses.GMP to format the ramanumbers for output, but can be built
entirely by itself: in that case, the ramanumbers are printed as
uint64:uint32.GMP to format the ramanumbers for output, but is otherwise
pretty self-containedIn all of the above data files, the format is:
S A1 B1 A2 B2 ...
where S = Ai3 + Bi3
for all i.
May 14, 2008
The tenth cabtaxi number is 933528127886302221000. For the full announcement which was posted to the NMBRTHRY mailing list, please click here
If you want to check my calculations (and I urge you to do so), I would suggest grabbing either the 4-way-and-higher numbers or the all-by-42 numbers and calculating some ranges. If you find any 4-way numbers that are not in my list, or you find more or less than 41 values between any two adjacent ones from the all-by-42 list, then either you or I will have screwed up... if you determine that it's me, then I would be very interested to hear from you.
April 2, 2008
No new data, just a bit of data-mining: I went looking for cube-free numbers among the triples-or-higher. I found 1370, of which 3 were quads:
| 1801049058342701083 | = 7 * 31 * 37 * 43 * 163 * 193 * 9151 * 18121 |
| = 922273 + 12165003 | |
| = 1366353 + 12161023 | |
| = 3419953 + 12076023 | |
| = 6002593 + 11658843 | |
| 682238339160892906483 | = 7 * 13 * 37 * 67 * 223 * 307 * 937 * 1693 * 27847 |
| = 23578353 + 87465523 | |
| = 47417043 + 83185393 | |
| = 52733553 + 81210523 | |
| = 68468593 + 71220843 | |
| 2724248230569896697541 | = 7 * 19 * 61 * 73 * 109 * 139 * 409 * 547 * 661 * 2053 |
| = 35157183 + 138916693 | |
| = 79750693 + 130393683 | |
| = 85187523 + 128180773 | |
| = 102308943 + 118246933 |
April 5, 2008: Christian Boyer informs me that the last of these has an additional decomposition as the sum of two cubes, just not positive ones: 415717813 - 410395503. So here we venture into the realm of cabtaxi numbers.
March 29, 2008
I have updated the big file containing the numbers that are equal to 42
mod 100: it is about 28 MB. Now all the files listed below
above contain the complete data from 1 to 2.4e22.
If you want to check my results (and I encourage you to do so), a
good place to start would be to work out how to do the calculations
just on numbers that are equal to some K mod N, then do a
run of values 42 mod 100 (this is why I added this big
file). The really really short version of how to do those calculations
is that you figure out which grid points yield the correct K in a
"unit cell", from (1,1) to (N,N), and then
for each of those active grid points, you step by N. For
N = 100, such a run should take roughly one to three
weeks on one computer. Note that N = 100 would not be
entirely an optimal choice for parallelizing the entire calculation,
as the work is not entirely uniform for all K; as it
happens, K = 42 does about half as much work as the
average, which is good for a verification run.
If you want some other value of K mod N, feel free to
contact me.
March 26, 2008
I have completed the scan of the range from 1 to 1e21; thus, the (small)
data files pointed at below above are now complete from 1
to 2.4e22 (I haven't yet updated the big one containing the numbers that are
equal to 42 mod 100).
March 9, 2008
The sixth taxicab number is 24153319581254312065344. For the full announcement which was posted to the NMBRTHRY mailing list, please click here