201:
72:. Other methods which guarantee that their result is prime, but which do not work for all primes, are useful for the random generation of provable primes.
133:
242:
160:
47:
266:
55:
271:
235:
150:
261:
177:
8:
216:
69:
50:
are the most common ways to generate provable primes for cryptography. Contrast with
228:
156:
129:
65:
212:
89:
84:
58:
51:
20:
255:
27:
39:
155:, Discrete Mathematics and Its Applications, CRC Press, pp. 124–125,
54:, which is likely (but not certain) to be prime, based on the output of a
43:
35:
108:
208:
75:
Provable primes have also been generated on embedded devices.
64:
In principle, every prime number can be proved to be prime in
113:, Philips Journal of Research, vol. 37, pp. 231–264
178:"Generating Provable Primes Efficiently on Embedded Devices"
16:
Prime integer calculated using a primality-proving algorithm
200:
111:
185:
123:
253:
236:
124:Crandall, Richard; Pomerance, Carl (2005).
243:
229:
126:Prime Numbers: A Computational Perspective
109:C. Couvreur and J. J. Quisquater (1982),
254:
175:
148:
195:
13:
46:. Boot-strapping techniques using
14:
283:
199:
152:RSA and Public-Key Cryptography
38:that has been calculated to be
169:
142:
128:. Springer. pp. 174–178.
117:
102:
1:
95:
215:. You can help Knowledge by
7:
149:Mollin, Richard A. (2002),
78:
10:
288:
194:
48:Pocklington primality test
42:using a primality-proving
18:
19:Not to be confused with
207:This article about a
176:Christophe, Clavier.
70:AKS primality test
224:
223:
279:
245:
238:
231:
203:
196:
189:
188:
182:
173:
167:
165:
146:
140:
139:
135:978-0387-25282-7
121:
115:
114:
106:
287:
286:
282:
281:
280:
278:
277:
276:
267:Primality tests
252:
251:
250:
249:
193:
192:
180:
174:
170:
163:
147:
143:
136:
122:
118:
107:
103:
98:
81:
66:polynomial time
24:
17:
12:
11:
5:
285:
275:
274:
269:
264:
248:
247:
240:
233:
225:
222:
221:
204:
191:
190:
168:
161:
141:
134:
116:
100:
99:
97:
94:
93:
92:
90:Primality test
87:
85:Probable prime
80:
77:
59:primality test
52:probable prime
32:provable prime
21:Probable prime
15:
9:
6:
4:
3:
2:
284:
273:
272:Prime numbers
270:
268:
265:
263:
260:
259:
257:
246:
241:
239:
234:
232:
227:
226:
220:
218:
214:
210:
205:
202:
198:
197:
186:
179:
172:
164:
162:9781420035247
158:
154:
153:
145:
137:
131:
127:
120:
112:
105:
101:
91:
88:
86:
83:
82:
76:
73:
71:
68:by using the
67:
62:
60:
57:
56:probabilistic
53:
49:
45:
41:
37:
33:
29:
28:number theory
22:
262:Number stubs
217:expanding it
206:
184:
171:
151:
144:
125:
119:
110:
104:
74:
63:
31:
25:
256:Categories
96:References
44:algorithm
79:See also
36:integer
209:number
159:
132:
34:is an
211:is a
181:(PDF)
40:prime
213:stub
157:ISBN
130:ISBN
30:, a
61:.
26:In
258::
183:.
244:e
237:t
230:v
219:.
187:.
166:.
138:.
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.