计
祡ぶ计
1905稲焊孽 (James Cullen 1867-1933) 矗闽猔 n*2n+1 计┦ (Primality)嘿 计 (Cullen Number) 癘 Cn τ讽い计獽琌计 (Cullen Prime)祇瞷讽 n 100 Cn 琌计Τ n = 1 ㎝ 53 ㄒC1 = 3 琌计C53 玥ゼだ侩ㄤ┦
ㄤБ圭 (Allan Joseph Champneys Cunningham 1842-1928) ―眔 C53 Τ琌 5591τ靡 C53 琌计 n 200 ずтぃ计暴ㄒ琌 n = 141 Б圭ゼ靡硂计琌计临琌计
τ碝т计陪眔殆Τ胔好ㄤ籔
筁緗猾还 (Raphael M. Robinson 1911-1994) 1957 靡 C141 琌计靡ウ琌 n 1000 ず暴计碝т计眔疭瘆秈甶筁1984惩扒 (Wilfrid Keller 1937- ) т计 n= 471357956611㎝ 18496讽硈 n = 1 ㎝ 141 硂 6 计癸莱 Cn 琌计Τ 6 计
计厩產璊 (Christopher Hooley) 矗碭┮Τ计计┏琌妮龟иごゼ絋﹚
计┦矗ボ
タБ圭┮ē计讽祡ぶ穦ぃ穦ΤΤ㎡硂琌ㄤいΤ砍届揭肈
и笵翴琌计砆 p = 2n-1 俱埃璝 p 琌 8k+3 ┪ 8k-3 ぇ计硂疭┦耞计┦Τ﹚ノ
и n = 1 10 ㄓボ
n |
Cn = n*2n+1 |
p = 2n-1 |
p ぇ┦ |
Cn ぇ┦ |
1 |
3 |
1 |
虫 |
计 |
2 |
9 |
3 |
计 (8k+3 ) |
计 (32) |
3 |
25 |
5 |
计 (8k-3 ) |
计 (52) |
4 |
65 |
7 |
计 |
计 (5*13) |
5 |
161 |
9 |
计 |
计 (7*23) |
6 |
385 |
11 |
计 (8k+3 ) |
计 (5*7*11) |
7 |
897 |
13 |
计 (8k-3 ) |
计 (3*13*23) |
8 |
2049 |
15 |
计 |
计 (3*683) |
9 |
4609 |
17 |
计 |
计 (11*419) |
10 |
10241 |
19 |
计 (8k+3 ) |
计 (72*11*19) |
把σゅ膍の呼
Ballinger, R. "Cullen Primes: Definition and Status." http://www.prothsearch.net/cullen.html.
Caldwell, C. K. "The Top Twenty: Cullen." http://primes.utm.edu/top20/page.php?id=6.
Guy, R. K. "Cullen Numbers." ”B20 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 77, 1994.
Hooley, C., Applications of sieve methods to the theory of numbers, Cambridge Tracts in Math. volume 70, Cambridge University Press, Cambridge, pp. xiv+122, 1976.
Robinson, R. M. "A report on primes of the form k*2n + 1 and on factors of Fermat numbers," Proc. Amer. Math. Soc., 9 p.673--681, 1958.
Weisstein, E. W. "Cullen Number." From MathWorld http://mathworld.wolfram.com/CullenNumber.html .