isprime - Maple Programming Help

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isprime

primality test

 Calling Sequence isprime(n)

Parameters

 n - integer

Description

 • The isprime command is a probabilistic primality testing routine. (See prime number.)
 • It returns false if n is shown to be composite within one strong pseudo-primality test and one Lucas test. It returns true otherwise.
 • If isprime returns true, n is very probably prime - see References section. No counterexample is known and it has been conjectured that such a counter example must be hundreds of digits long.

Examples

 > $\mathrm{isprime}\left(1\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{isprime}\left(2\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{isprime}\left(17\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{isprime}\left(21\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{isprime}\left(11!+1\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{isprime}\left({2}^{30}{3}^{30}+7\right)$
 ${\mathrm{true}}$ (6)

The Tabulate command can be used to display prime numbers in a grid. The following table highlights any prime numbers with a pink background.

 > $V≔\left(r,c\right)↦\mathrm{DocumentTools}:-\mathrm{Tabulate}\left(\mathrm{Matrix}\left(r,c,\left(i,j\right)↦c\cdot \left(i-1\right)+j\right),\mathrm{fillcolor}=\left(\left(T,i,j\right)↦\mathrm{if}\left(\mathrm{isprime}\left(c\cdot \left(i-1\right)+j\right),"Pink","White"\right)\right)\right):$
 > $V\left(10,30\right)$
 ${"Tabulate"}$ (7)

 $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $11$ $12$ $13$ $14$ $15$ $16$ $17$ $18$ $19$ $20$ $21$ $22$ $23$ $24$ $25$ $26$ $27$ $28$ $29$ $30$ $31$ $32$ $33$ $34$ $35$ $36$ $37$ $38$ $39$ $40$ $41$ $42$ $43$ $44$ $45$ $46$ $47$ $48$ $49$ $50$ $51$ $52$ $53$ $54$ $55$ $56$ $57$ $58$ $59$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$ $69$ $70$ $71$ $72$ $73$ $74$ $75$ $76$ $77$ $78$ $79$ $80$ $81$ $82$ $83$ $84$ $85$ $86$ $87$ $88$ $89$ $90$ $91$ $92$ $93$ $94$ $95$ $96$ $97$ $98$ $99$ $100$ $101$ $102$ $103$ $104$ $105$ $106$ $107$ $108$ $109$ $110$ $111$ $112$ $113$ $114$ $115$ $116$ $117$ $118$ $119$ $120$ $121$ $122$ $123$ $124$ $125$ $126$ $127$ $128$ $129$ $130$ $131$ $132$ $133$ $134$ $135$ $136$ $137$ $138$ $139$ $140$ $141$ $142$ $143$ $144$ $145$ $146$ $147$ $148$ $149$ $150$ $151$ $152$ $153$ $154$ $155$ $156$ $157$ $158$ $159$ $160$ $161$ $162$ $163$ $164$ $165$ $166$ $167$ $168$ $169$ $170$ $171$ $172$ $173$ $174$ $175$ $176$ $177$ $178$ $179$ $180$ $181$ $182$ $183$ $184$ $185$ $186$ $187$ $188$ $189$ $190$ $191$ $192$ $193$ $194$ $195$ $196$ $197$ $198$ $199$ $200$ $201$ $202$ $203$ $204$ $205$ $206$ $207$ $208$ $209$ $210$ $211$ $212$ $213$ $214$ $215$ $216$ $217$ $218$ $219$ $220$ $221$ $222$ $223$ $224$ $225$ $226$ $227$ $228$ $229$ $230$ $231$ $232$ $233$ $234$ $235$ $236$ $237$ $238$ $239$ $240$ $241$ $242$ $243$ $244$ $245$ $246$ $247$ $248$ $249$ $250$ $251$ $252$ $253$ $254$ $255$ $256$ $257$ $258$ $259$ $260$ $261$ $262$ $263$ $264$ $265$ $266$ $267$ $268$ $269$ $270$ $271$ $272$ $273$ $274$ $275$ $276$ $277$ $278$ $279$ $280$ $281$ $282$ $283$ $284$ $285$ $286$ $287$ $288$ $289$ $290$ $291$ $292$ $293$ $294$ $295$ $296$ $297$ $298$ $299$ $300$

 > 

Note that this procedure can be modified to show tables for various values of r and c.

References

 Knuth, Donald E. The Art of Computer Programming. 2nd ed. Reading, Mass.: Addison-Wesley, 1997. Vol. 2 Section 4.5.4: Algorithm P.
 Riesel, H. Prime Numbers and Computer Methods for Factorization. Basel: Birkhauser, 1994.