EE4253 Digital Communications
Prime Polynomials (2..511)

Binary values expressed as polynomials can readily be manipulated using the rules of binary arithmetic.

The table below shows all prime polynomials from 2..511. (note these do not always correspond to the prime integers!). Try the LRS link to see the corresponding Linear Recursive Sequence. Polynomials leading to maximum length sequences are shown highlighted. For larger numbers, try the Online Factoring Tool

See all polynomials from 0..127

NUMBERBINARY POLYNOMIAL PRIME FACTORS
2. 10 x prime [ LRS ]
3. 11 x+1 prime [ LRS ] *
7. 111 x2+x+1 prime [ LRS ] *
11. 1011 x3+x+1 prime [ LRS ] *
13. 1101 x3+x2+1 prime [ LRS ] *
19. 10011 x4+x+1 prime [ LRS ] *
25. 11001 x4+x3+1 prime [ LRS ] *
31. 11111 x4+x3+x2+x+1 prime [ LRS ]
37. 100101 x5+x2+1 prime [ LRS ] *
41. 101001 x5+x3+1 prime [ LRS ] *
47. 101111 x5+x3+x2+x+1 prime [ LRS ] *
55. 110111 x5+x4+x2+x+1 prime [ LRS ] *
59. 111011 x5+x4+x3+x+1 prime [ LRS ] *
61. 111101 x5+x4+x3+x2+1 prime [ LRS ] *
67. 1000011 x6+x+1 prime [ LRS ] *
73. 1001001 x6+x3+1 prime [ LRS ]
87. 1010111 x6+x4+x2+x+1 prime [ LRS ]
91. 1011011 x6+x4+x3+x+1 prime [ LRS ] *
97. 1100001 x6+x5+1 prime [ LRS ] *
103. 1100111 x6+x5+x2+x+1 prime [ LRS ] *
109. 1101101 x6+x5+x3+x2+1 prime [ LRS ] *
115. 1110011 x6+x5+x4+x+1 prime [ LRS ] *
117. 1110101 x6+x5+x4+x2+1 prime [ LRS ]
131. 10000011 x7+x+1 prime [ LRS ] *
137. 10001001 x7+x3+1 prime [ LRS ] *
143. 10001111 x7+x3+x2+x+1 prime [ LRS ] *
145. 10010001 x7+x4+1 prime [ LRS ] *
157. 10011101 x7+x4+x3+x2+1 prime [ LRS ] *
167. 10100111 x7+x5+x2+x+1 prime [ LRS ] *
171. 10101011 x7+x5+x3+x+1 prime [ LRS ] *
185. 10111001 x7+x5+x4+x3+1 prime [ LRS ] *
191. 10111111 x7+x5+x4+x3+x2+x+1 prime [ LRS ] *
193. 11000001 x7+x6+1 prime [ LRS ] *
203. 11001011 x7+x6+x3+x+1 prime [ LRS ] *
211. 11010011 x7+x6+x4+x+1 prime [ LRS ] *
213. 11010101 x7+x6+x4+x2+1 prime [ LRS ] *
229. 11100101 x7+x6+x5+x2+1 prime [ LRS ] *
239. 11101111 x7+x6+x5+x3+x2+x+1 prime [ LRS ] *
241. 11110001 x7+x6+x5+x4+1 prime [ LRS ] *
247. 11110111 x7+x6+x5+x4+x2+x+1 prime [ LRS ] *
253. 11111101 x7+x6+x5+x4+x3+x2+1 prime [ LRS ] *
283. 100011011 x8+x4+x3+x+1 prime [ LRS ]
285. 100011101 x8+x4+x3+x2+1 prime [ LRS ] *
299. 100101011 x8+x5+x3+x+1 prime [ LRS ] *
301. 100101101 x8+x5+x3+x2+1 prime [ LRS ] *
313. 100111001 x8+x5+x4+x3+1 prime [ LRS ]
319. 100111111 x8+x5+x4+x3+x2+x+1 prime [ LRS ]
333. 101001101 x8+x6+x3+x2+1 prime [ LRS ] *
351. 101011111 x8+x6+x4+x3+x2+x+1 prime [ LRS ] *
355. 101100011 x8+x6+x5+x+1 prime [ LRS ] *
357. 101100101 x8+x6+x5+x2+1 prime [ LRS ] *
361. 101101001 x8+x6+x5+x3+1 prime [ LRS ] *
369. 101110001 x8+x6+x5+x4+1 prime [ LRS ] *
375. 101110111 x8+x6+x5+x4+x2+x+1 prime [ LRS ]
379. 101111011 x8+x6+x5+x4+x3+x+1 prime [ LRS ]
391. 110000111 x8+x7+x2+x+1 prime [ LRS ] *
395. 110001011 x8+x7+x3+x+1 prime [ LRS ]
397. 110001101 x8+x7+x3+x2+1 prime [ LRS ] *
415. 110011111 x8+x7+x4+x3+x2+x+1 prime [ LRS ]
419. 110100011 x8+x7+x5+x+1 prime [ LRS ]
425. 110101001 x8+x7+x5+x3+1 prime [ LRS ] *
433. 110110001 x8+x7+x5+x4+1 prime [ LRS ]
445. 110111101 x8+x7+x5+x4+x3+x2+1 prime [ LRS ]
451. 111000011 x8+x7+x6+x+1 prime [ LRS ] *
463. 111001111 x8+x7+x6+x3+x2+x+1 prime [ LRS ] *
471. 111010111 x8+x7+x6+x4+x2+x+1 prime [ LRS ]
477. 111011101 x8+x7+x6+x4+x3+x2+1 prime [ LRS ]
487. 111100111 x8+x7+x6+x5+x2+x+1 prime [ LRS ] *
499. 111110011 x8+x7+x6+x5+x4+x+1 prime [ LRS ]
501. 111110101 x8+x7+x6+x5+x4+x2+1 prime [ LRS ] *
505. 111111001 x8+x7+x6+x5+x4+x3+1 prime [ LRS ]

17 NOV 03 - R.Tervo EE4253
University of New Brunswick, Department of Electrical and Computer Engineering