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 ㄒC1 = 3 琌计C53 玥ゼだ侩ㄤ┦

ㄤБ圭 (Allan Joseph Champneys Cunningham 1842-1928) ―眔 C53 Τ琌 5591τ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= 471357956611㎝ 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 .