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One example Guy gives is the conjecture that is prime—in fact, a Mersenne prime—when is prime; but this conjecture, while true for = 2, 3, 5 and 7, fails for = 11 (and for many other values). Another relates to the prime number race : primes congruent to 3 modulo 4 appear to be more numerous than those congruent to 1; however this is false ...
Angular unconformities can occur in ash fall layers of pyroclastic rock deposited by volcanoes during explosive eruptions. In these cases, the hiatus in deposition represented by the unconformity may be geologically very short – hours, days or weeks.
The tendency for an initial segment of data to show some bias that drops out later, one example in number theory being Kummer's conjecture on cubic Gauss sums; The strong law of small numbers, an observation made by the mathematician Richard K. Guy: "There aren't enough small numbers to meet the many demands made of them."
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
For this reason, it is more accurately called "Pólya's problem". The size of the smallest counterexample is often used to demonstrate the fact that a conjecture can be true for many cases and still fail to hold in general, [ 2 ] providing an illustration of the strong law of small numbers .
This is exploited by birthday attacks on cryptographic hash functions and is the reason why a small number of collisions in a hash table are, for all practical purposes, inevitable. The theory behind the birthday problem was used by Zoe Schnabel [18] under the name of capture-recapture statistics to estimate the size of fish population in lakes ...
Although they are small, melt inclusions may contain a number of different constituents, including glass (which represents magma that has been quenched by rapid cooling), small crystals and a separate vapour-rich bubble. They occur in most of the crystals found in igneous rocks and are common in the minerals quartz, feldspar, olivine and pyroxene.
Murphy's law [a] is an adage or epigram that is typically stated as: "Anything that can go wrong will go wrong.".. Though similar statements and concepts have been made over the course of history, the law itself was coined by, and named after, American aerospace engineer Edward A. Murphy Jr.; its exact origins are debated, but it is generally agreed it originated from Murphy and his team ...