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These are large numbers that are related to unsolved problems. Some of these values are subject to change, e.g. bounds on solutions. |
These are large numbers that are related to unsolved problems. Some of these values are subject to change, e.g. bounds on solutions. |
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*If odd perfect numbers exist, they must be at least as large as \(10^{1500}\)<ref>P. Ochem, M. Rao, [https://www.ams.org/journals/mcom/2012-81-279/S0025-5718-2012-02563-4/S0025-5718-2012-02563-4.pdf Odd perfect numbers are greater than 10^1500] (2012, accessed 2020-11-11)</ref>. |
*If odd perfect numbers exist, they must be at least as large as \(10^{1500}\)<ref>P. Ochem, M. Rao, [https://www.ams.org/journals/mcom/2012-81-279/S0025-5718-2012-02563-4/S0025-5718-2012-02563-4.pdf Odd perfect numbers are greater than 10^1500] (2012, accessed 2020-11-11)</ref>. |
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| − | *If [[Numbers from Singmaster's conjecture|Singmaster's conjecture]] holds for \(N=6\), then the second smallest number that satisfies this condition is \(61,218,182,743,304,701,891,431,482,520\approx 6.12\times 10^{28}\)<ref>T. D. Noe, [https://oeis.org/A003015 Remark on sequence A003015] (2004)</ref> |
+ | *If [[Numbers from Singmaster's conjecture|Singmaster's conjecture]] holds for \(N=6\), then the second smallest number that satisfies this condition in Pascal's triangle is \(61,218,182,743,304,701,891,431,482,520\approx 6.12\times 10^{28}\)<ref>T. D. Noe, [https://oeis.org/A003015 Remark on sequence A003015] (2004)</ref> |
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[[Category:Lists]] |
[[Category:Lists]] |
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Revision as of 00:52, 12 November 2020
These are large numbers that are related to unsolved problems. Some of these values are subject to change, e.g. bounds on solutions.
- If odd perfect numbers exist, they must be at least as large as \(10^{1500}\)[1].
- If Singmaster's conjecture holds for \(N=6\), then the second smallest number that satisfies this condition in Pascal's triangle is \(61,218,182,743,304,701,891,431,482,520\approx 6.12\times 10^{28}\)[2]
- ↑ P. Ochem, M. Rao, Odd perfect numbers are greater than 10^1500 (2012, accessed 2020-11-11)
- ↑ T. D. Noe, Remark on sequence A003015 (2004)