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	zptest.3 - libzahl - big integer library
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	zptest.3 (1512B)
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	1 .TH ZPTEST 3 libzahl
	2 .SH NAME
	3 zptest - Test the primality of a big integer
	4 .SH SYNOPSIS
	5 .nf
	6 #include <zahl.h>
	7
	8 enum zprimality zptest(z_t \fIwitness\fP, z_t \fIquestioned\fP, int \fIt…
	9 .fi
	10 .SH DESCRIPTION
	11 .B zptest
	12 tests whether
	13 .I questioned
	14 is a prime number. This is implemented using the
	15 Miller–Rabin primality test.
	16 .P
	17 If
	18 .I questioned
	19 is determined to be a composite, the witness if its
	20 compositeness is stored into
	21 .I witness
	22 unless
	23 .I witness
	24 is
	25 .BR 0 .
	26 .BR zgcd (3)
	27 can be used on
	28 .I questioned
	29 and
	30 .I witness
	31 to extract a factor of
	32 .IR questioned .
	33 This factor can be either composite, prime, or 1.
	34 .P
	35 The risk that a composite number is determined to be
	36 a probably prime is
	37 .IR (1-4↑-tries) .
	38 .P
	39 It is safe to call
	40 .B zptest
	41 with non-unique parameters, and with
	42 .IR "(witness==0)" .
	43 .SH RETURN VALUE
	44 This function will either return:
	45 .TP
	46 .B NONPRIME
	47 .I questioned
	48 is certainly a nonprime number (composite).
	49 .TP
	50 .B PROBABLY_PRIME
	51 .I questioned
	52 is probably a prime number.
	53 .TP
	54 .B PRIME
	55 .I questioned
	56 is certainly a prime number.
	57 .SH NOTES
	58 If
	59 .I questioned
	60 is less than two
	61 .I questioned
	62 is copied into
	63 .P
	64 Increasing
	65 .I tries
	66 only reduces the chance that
	67 .B PROBABLY_PRIME
	68 is returned. It cannot increase
	69 the chance that
	70 .B PRIME
	71 is returned.
	72 .IR witness .
	73 .SH RATIONALE
	74 .B NONPRIME
	75 is called just that, rather than COMPOSITE,
	76 because negative integers, zero, and one are
	77 neither prime nor composite. (One was historically
	78 a prime, we do not recognise it as such.)
	79 .SH SEE ALSO
	80 .BR zgcd (3)