Number fragmentation

One of the most commonly used hash algorithm employs twin prime numbers (two consecutive odd numbers that are both primes) and modulo function. If KEY is a large number (fragment ID or XOR-ed parts of chopped long string) and NP the length of the direct access file than the calculated address ADDR and the increment INCR can be obtained by the following equations ... 

Mass spectrum The MS shows an odd molecular weight at 121 and a large even-numbered fragment at 106. These features may indicate the presence of a nitrogen atom. 

All of the inositol stereoisomers have been investigated, as their trimethylsilyl ethers and as their acetates, by g.I.c.-m.s. The inositol hexaacetates give two main fragmentation series, and these were studied by deuterium-labelling experiments. In one series, the molecular ion (very weak) undergoes consecutive losses of ketene or acetic acid to give a series of even-numbered fragments (see Scheme 30). 

Consequently, the number of elementary units which are found associated in i-numbered fragments is given by... 

Now there is the further condition that the sum of all 1, 2, 3 etc. numbered fragments times their numerical index must be equal to the number of units present in the beginning, a requirement which may be confirmed easily by a short calculation. 

Large number of even-numbered fragment ions... 

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