COMMENT ⊗   VALID 00007 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	\input acphdr % This file contains material to be set out of normal sequence
C00003 00003	% Table 1 from Section 3.2.1.1	*
C00011 00004	% Table 3.3.4-1 (goes on top of two facing pages)	*
C00022 00005	% Table 1 from Section 4.3.3	*
C00025 00006	% Table 1 from Section 4.5.4	*
C00030 00007	\eject % eject previous page
C00031 ENDMK
C⊗;
\input acphdr % This file contains material to be set out of normal sequence
\titlepage\setcount00
\null
\vfill
\tenpoint
\ctrline{Volume 2 of THE ART OF COMPUTER PROGRAMMING}
\ctrline{---special material set out of normal sequence---}
\ctrline{$\copyright$ 1978 Addison--Wesley Publishing Company, Inc.}
\vfill
\runninglefthead{RANDOM NUMBERS}
% The page numbers may need to be changed
% Table 1 from Section 3.2.1.1	*
\runningrighthead{CHOICE OF MODULUS}
\section{3.2.1.1}
\eject % eject the previous page
\acpmark{\chd}{\csec}
\setcount0 13
\tablehead{Table 1}
\penalty1000
\vfill
\ninepoint\ctrline{PRIME FACTORIZATIONS OF $w \pm 1$}
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\vskip-2pt
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⊗\¬⊗⊗\¬\cr
7 \cdot 31 \cdot 151⊗\\⊗15⊗\\⊗3↑2 \cdot 11 \cdot 331\cr
3 \cdot 5 \cdot 17 \cdot 257⊗\\⊗16⊗\\⊗65537\cr
131071⊗\\⊗17⊗\\⊗3 \cdot 43691\cr
3↑3 \cdot 7 \cdot 19 \cdot 73⊗\\⊗18⊗\\⊗5 \cdot 13 \cdot 37 \cdot 109\cr
524287⊗\\⊗19⊗\\⊗3 \cdot 174763\cr
3 \cdot 5↑2 \cdot 11 \cdot 31 \cdot 41⊗\\⊗20⊗\\⊗17 \cdot 61681\cr
7↑2 \cdot 127 \cdot 337⊗\\⊗21⊗\\⊗3↑2 \cdot 43 \cdot 5419\cr
3 \cdot 23 \cdot 89 \cdot 683⊗\\⊗22⊗\\⊗5 \cdot 397 \cdot 2113\cr
47 \cdot 178481⊗\\⊗23⊗\\⊗3 \cdot 2796203\cr
3↑2 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \cdot 241⊗\\⊗24⊗\\⊗97 \cdot 257 \cdot 673\cr
31 \cdot 601 \cdot 1801⊗\\⊗25⊗\\⊗3 \cdot 11 \cdot 251 \cdot 4051\cr
3 \cdot 2731 \cdot 8191⊗\\⊗26⊗\\⊗5 \cdot 53 \cdot 157 \cdot 1613\cr
7 \cdot 73 \cdot 262657⊗\\⊗27⊗\\⊗3↑4 \cdot 19 \cdot 87211\cr
3 \cdot 5 \cdot 29 \cdot 43 \cdot 113 \cdot 127⊗\\⊗28⊗\\⊗17 \cdot 15790321\cr
233 \cdot 1103 \cdot 2089⊗\\⊗29⊗\\⊗3 \cdot 59 \cdot 3033169\cr
3↑2 \cdot 7 \cdot 11 \cdot 31 \cdot 151 \cdot 331⊗\\⊗30⊗\\⊗5↑2 \cdot
	13 \cdot 41 \cdot 61 \cdot 1321\cr
2147483647⊗\\⊗31⊗\\⊗3 \cdot 715827883\cr
3 \cdot 5 \cdot 17 \cdot 257 \cdot 65537⊗\\⊗32⊗\\⊗641 \cdot 6700417\cr
7 \cdot 23 \cdot 89 \cdot 599479⊗\\⊗33⊗\\⊗3↑2 \cdot 67 \cdot 683 \cdot 20857\cr
3 \cdot 43691 \cdot 131071⊗\\⊗34⊗\\⊗5 \cdot 137 \cdot 953 \cdot 26317\cr
31 \cdot 71 \cdot 127 \cdot 122921⊗\\⊗35⊗\\⊗3 \cdot 11 \cdot 43 \cdot
	281 \cdot 86171\cr
3↑2 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \cdot 37 \cdot 73 \cdot
	109⊗\\⊗36⊗\\⊗17 \cdot 241 \cdot 433 \cdot 38737\cr
223 \cdot 616318177⊗\\⊗37⊗\\⊗3 \cdot 1777 \cdot 25781083\cr
3 \cdot 174763 \cdot 524287⊗\\⊗38⊗\\⊗5 \cdot 229 \cdot 457 \cdot 525313\cr
7 \cdot 79 \cdot 8191 \cdot 121369⊗\\⊗39⊗\\⊗3↑2 \cdot 2731 \cdot 22366891\cr
3 \cdot 5↑2 \cdot 11 \cdot 17 \cdot 31 \cdot 41 \cdot 61681⊗\\⊗40⊗\\⊗257
	\cdot 4278255361\cr
13367 \cdot 164511353⊗\\⊗41⊗\\⊗3 \cdot 83 \cdot 8831418697\cr
3↑2 \cdot 7↑2 \cdot 43 \cdot 127 \cdot 337 \cdot 5419⊗\\⊗42⊗\\⊗5 \cdot
	13 \cdot 29 \cdot 113 \cdot 1429 \cdot 14449\cr
431 \cdot 9719 \cdot 2099863⊗\\⊗43⊗\\⊗3 \cdot 2932031007403\cr
3 \cdot 5 \cdot 23 \cdot 89 \cdot 397 \cdot 683 \cdot 2113⊗\\⊗44⊗\\⊗17
	\cdot 353 \cdot 2931542417\cr
7 \cdot 31 \cdot 73 \cdot 151 \cdot 631 \cdot 23311⊗\\⊗45⊗\\⊗3↑3 \cdot
	11 \cdot 19 \cdot 331 \cdot 18837001\cr
3 \cdot 47 \cdot 178481 \cdot 2796203⊗\\⊗46⊗\\⊗5 \cdot 277 \cdot 1013
	\cdot 1657 \cdot 30269\cr
2351 \cdot 4513 \cdot 13264529⊗\\⊗47⊗\\⊗3 \cdot 283 \cdot 165768537521\cr
3↑2 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \cdot 97 \cdot 241 \cdot
	257 \cdot 673⊗\\⊗48⊗\\⊗193 \cdot 65537 \cdot 22253377\cr
179951 \cdot 3203431780337⊗\\⊗59⊗\\⊗3 \cdot 2833 \cdot 37171 \cdot 1824726041\cr
3↑2 \cdot 5↑2 \cdot 7 \cdot 11 \cdot 13 \cdot 31 \cdot 41 \cdot
	61 \cdot 151 \cdot 331 \cdot 1321⊗\\⊗60⊗\\⊗17 \cdot 241 \cdot 61681
	\cdot 4562284561\cr
7↑2 \cdot 73 \cdot 127 \cdot 337 \cdot 92737
	\cdot 649657⊗\\⊗63⊗\\⊗3↑3 \cdot 19 \cdot 43 \cdot 5419 \cdot 77158673929\cr
3 \cdot 5 \cdot 17 \cdot 257 \cdot 641 \cdot 65537 \cdot 6700417⊗\\⊗64⊗\\⊗274177
	\cdot 67280421310721\cr
⊗\¬⊗⊗\¬\cr
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3↑3 \cdot 7 \cdot 11 \cdot 13 \cdot 37⊗\\⊗\96⊗\\⊗101 \cdot 9901\cr
3↑2 \cdot 239 \cdot 4649⊗\\⊗\97⊗\\⊗11 \cdot 909091\cr
3↑2 \cdot 11 \cdot 73 \cdot 101 \cdot 137⊗\\⊗\98⊗\\⊗17 \cdot 5882353\cr
3↑4 \cdot 37 \cdot 333667⊗\\⊗\99⊗\\⊗7 \cdot 11 \cdot 13 \cdot 19 \cdot 52579\cr
3↑2 \cdot 11 \cdot 41 \cdot 271 \cdot 9091⊗\\⊗10⊗\\⊗101 \cdot 3541
	\cdot 27961\cr
3↑2 \cdot 21649 \cdot 513239⊗\\⊗11⊗\\⊗11↑2 \cdot 23 \cdot 4093 \cdot 8779\cr
3↑3 \cdot 7 \cdot 11 \cdot 13 \cdot 37 \cdot 101 \cdot 9901⊗\\⊗12⊗\\⊗73
	\cdot 137 \cdot 99990001\cr
3↑2 \cdot 11 \cdot 17 \cdot 73 \cdot 101 \cdot
	137 \cdot 5882353⊗\\⊗16⊗\\⊗353 \cdot 449 \cdot 641 \cdot 1409 \cdot 69857\cr
⊗\¬⊗⊗\¬\cr
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% Table 3.3.4-1 (goes on top of two facing pages)	*
% This table is accounted for by two topinserts of height 360pt
\runningrighthead{THE SPECTRAL TEST}
\section{3.3.4}
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1⊗23 ⊗10↑8 + 1⊗530 ⊗530 ⊗530 ⊗530 ⊗447 \cr
2⊗2↑7 + 1⊗2↑{35}⊗16642 ⊗16642 ⊗16642 ⊗15602 ⊗252 \cr
3⊗2↑{18} + 1⊗2↑{35}⊗34359738368 ⊗6 ⊗4 ⊗4 ⊗4 \cr
4⊗3141592653 ⊗2↑{35}⊗2997222016 ⊗1026050 ⊗27822 ⊗1118 ⊗1118 \cr
5⊗137 ⊗256⊗274 ⊗30 ⊗14 ⊗6 ⊗4 \cr
6⊗3141592621 ⊗10↑{10}⊗4577114792 ⊗1034718 ⊗62454 ⊗1776 ⊗542 \cr
7⊗3141592221 ⊗10↑{10}⊗4293881050 ⊗276266 ⊗97450 ⊗3366 ⊗2382 \cr
8⊗6180339881 ⊗10↑{10}⊗1732237138 ⊗3880616 ⊗17786 ⊗8244 ⊗938 \cr
9⊗4160984121 ⊗10↑{10}⊗9183801602 ⊗4615650 ⊗16686 ⊗6840 ⊗1344 \cr
10⊗3141592221 ⊗2↑{35}⊗13539813818 ⊗5795090 ⊗88134 ⊗12716 ⊗2938 \cr
11⊗271828129 ⊗2↑{35}⊗22939188896 ⊗2723830 ⊗146116 ⊗10782 ⊗2914 \cr
12⊗5↑{13}⊗2↑{35}⊗33161885770 ⊗2925242 ⊗113374 ⊗13070 ⊗2256 \cr
13⊗5↑{15}⊗2↑{35}⊗22078865098 ⊗10274746 ⊗167558 ⊗5844 ⊗2592 \cr
14⊗2↑{23} + 2↑{12} + 5⊗2↑{35}⊗167510120 ⊗8052254 ⊗21476 ⊗16802
⊗1630 \cr
15⊗2↑{23} + 2↑{13} + 5⊗2↑{35}⊗168231328 ⊗5335322 ⊗21476 ⊗2008
⊗1134 \cr
16⊗2↑{23} + 2↑{14} + 5⊗2↑{35}⊗12256151168 ⊗5733878 ⊗21476 ⊗13316
⊗2032 \cr
17⊗2↑{22} + 2↑{13} + 5⊗2↑{35}⊗8201443840 ⊗1830230 ⊗21476 ⊗7786
⊗3080 \cr
18⊗2↑{24} + 2↑{13} + 5⊗2↑{35}⊗8364058⊗8364058⊗21476 ⊗16712 ⊗1496 \cr
19⊗21235486157 ⊗2↑{35}⊗14742505450 ⊗5305448 ⊗165818 ⊗12062 ⊗1706 \cr
20⊗1175245817 ⊗2↑{35}⊗36336418002 ⊗7362242 ⊗95306 ⊗3006 ⊗2860 \cr
21⊗17059465 ⊗2↑{35}⊗39341117000 ⊗9476606 ⊗202796 ⊗18758 ⊗2382 \cr
22⊗2↑{16} + 3⊗2↑{29}⊗536805386 ⊗118 ⊗116 ⊗116 ⊗116 \cr
23⊗2654435769 ⊗2↑{32}⊗3606635378 ⊗2027906 ⊗23838 ⊗2032 ⊗286 \cr
24⊗1566083941 ⊗2↑{32}⊗4659748970 ⊗2079590 ⊗44902 ⊗4652 ⊗662 \cr
25⊗69069 ⊗2↑{32}⊗4243209856 ⊗2072544 ⊗52804 ⊗6990 ⊗242 \cr
26⊗1664525 ⊗2↑{32}⊗4938916874 ⊗2322494 ⊗63712 ⊗4092 ⊗1038 \cr
27⊗314159269 ⊗2↑{31} - 1⊗143232969 ⊗899290 ⊗36985 ⊗3427 ⊗1144 \cr
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29⊗31167285 ⊗2↑{48}⊗3.2 \times 10↑{14}⊗4111841446 ⊗17341510
⊗306326 ⊗59278 \cr
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4.5⊗4.5⊗4.5⊗4.5⊗4.4⊗2\epsilon↑5⊗5\epsilon↑4⊗0.01⊗0.34⊗4.62⊗1\cr
7.0⊗7.0⊗7.0⊗7.0⊗4.0⊗2\epsilon↑6⊗3\epsilon↑4⊗0.04⊗4.66⊗2\epsilon
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17.5⊗1.3⊗1.0⊗1.0⊗1.0⊗3.14⊗2\epsilon↑9⊗2\epsilon↑9⊗5\epsilon
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15.7⊗10.0⊗7.4⊗5.0⊗5.0⊗0.27⊗0.13⊗0.11⊗0.01⊗0.21⊗4\cr
4.0⊗2.5⊗1.9⊗1.3⊗1.0⊗3.36⊗2.69⊗3.78⊗1.81⊗1.29⊗5\cr
16.0⊗10.0⊗8.0⊗5.4⊗4.5⊗1.44⊗0.44⊗1.92⊗0.07⊗0.08⊗6\cr
16.0⊗9.0⊗8.3⊗5.9⊗5.6⊗1.35⊗0.06⊗4.69⊗0.35⊗6.98⊗7\cr
15.3⊗10.9⊗7.1⊗6.5⊗4.9⊗0.54⊗3.20⊗0.16⊗3.25⊗0.43⊗8\cr
16.5⊗11.1⊗7.0⊗6.4⊗5.2⊗2.89⊗4.15⊗0.14⊗2.04⊗1.25⊗9\cr
16.8⊗11.2⊗8.2⊗6.8⊗5.8⊗1.24⊗1.70⊗1.12⊗2.79⊗3.81⊗10\cr
17.2⊗10.7⊗8.6⊗6.7⊗5.8⊗2.10⊗0.55⊗3.15⊗1.85⊗3.72⊗11\cr
17.5⊗10.7⊗8.4⊗6.8⊗5.6⊗3.03⊗0.61⊗1.85⊗2.99⊗1.73⊗12\cr
17.2⊗11.6⊗8.7⊗6.3⊗5.7⊗2.02⊗4.02⊗4.03⊗0.40⊗2.62⊗13\cr
13.7⊗11.5⊗7.2⊗7.0⊗5.3⊗0.02⊗2.79⊗0.07⊗5.61⊗0.65⊗14\cr
13.7⊗11.2⊗7.2⊗5.5⊗5.1⊗0.02⊗1.50⊗0.07⊗0.03⊗0.22⊗15\cr
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16.9⊗11.2⊗8.7⊗6.8⊗5.4⊗1.35⊗1.50⊗3.95⊗2.45⊗0.75⊗19\cr
17.5⊗11.4⊗8.3⊗5.8⊗5.7⊗3.33⊗2.44⊗1.30⊗0.08⊗3.52⊗20\cr
17.6⊗11.6⊗8.8⊗7.1⊗5.6⊗3.60⊗3.56⊗5.91⊗7.38⊗2.03⊗21\cr
14.5⊗3.4⊗3.4⊗3.4⊗3.4⊗3.14⊗\epsilon↑5⊗\epsilon↑4⊗\epsilon
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15.9⊗10.5⊗7.3⊗5.5⊗4.1⊗2.64⊗2.82⊗0.65⊗0.23⊗0.03⊗23\cr
31.0⊗20.2⊗15.6⊗11.8⊗9.8⊗3.14⊗1.49⊗0.44⊗0.69⊗0.66⊗24\cr
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16.1⊗10.5⊗7.7⊗6.1⊗4.7⊗3.41⊗2.92⊗2.32⊗1.81⊗0.35⊗28\cr
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\hjust to 28pt{\hfill\hskip-4pt14.89\hfill}\!
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\vfill % end right half of table
% Table 1 from Section 4.3.3	*
\runninglefthead{ARITHMETIC}
\runningrighthead{HOW FAST CAN WE MULTIPLY\:a?}
\section{4.3.3}
\eject % eject the previous page
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\setcount0 296
\tablehead{Table 1}
\penalty1000
\vfill
\ninepoint\ctrline{MULTIPLICATION IN A LINEAR ITERATIVE ARRAY}
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⊗\hfill#\hfill⊗\hfill#\hfill⊗\hfill#\hfill⊗\hfill#\hfill\tabskip0pt\cr
Time⊗Input⊗Module $M↓1$⊗Module $M↓2$⊗Module $M↓3$\cr
\noalign{\vskip 3pt\hrule\vskip 3pt}
⊗\\{u↓j}{v↓j}{q↓j}⊗\!
\[c{x↓0}{y↓0}{x↓1}{y↓1}xy{z↓2}{z↓1}{z↓0}]⊗\!
\[c{x↓0}{y↓0}{x↓1}{y↓1}xy{z↓2}{z↓1}{z↓0}]⊗\!
\[c{x↓0}{y↓0}{x↓1}{y↓1}xy{z↓2}{z↓1}{z↓0}]\cr
\noalign{\vskip 3pt\hrule\vskip 3pt}
\90⊗\\111⊗\[0000000000]⊗\[0000000000]⊗\[0000000000]\cr
\91⊗\\111⊗\[1110000010]⊗\[0000000000]⊗\[0000000000]\cr
\92⊗\\110⊗\[2111100100]⊗\[0000000000]⊗\[0000000000]\cr
\93⊗\\001⊗\[3111111011]⊗\[0000000001]⊗\[0000000000]\cr
\94⊗\\110⊗\[3111100101]⊗\[1110000001]⊗\[0000000000]\cr
\95⊗\\000⊗\[3111111011]⊗\[2110000001]⊗\[0000000000]\cr
\96⊗\\000⊗\[3111100100]⊗\[3110011010]⊗\[0000000000]\cr
\97⊗\\000⊗\[3111100000]⊗\[3110000010]⊗\[1110000001]\cr
\98⊗\\000⊗\[3111100000]⊗\[3110000010]⊗\[2110000000]\cr
\99⊗\\000⊗\[3111100000]⊗\[3110000001]⊗\[3110000000]\cr
10⊗\\000⊗\[3111100001]⊗\[3110000000]⊗\[3110000000]\cr
11⊗\\000⊗\[3111100000]⊗\[3110000000]⊗\[3110000000]\cr}
\lineskip0pt
% Table 1 from Section 4.5.4	*
\runninglefthead{ARITHMETIC}
\runningrighthead{FACTORING INTO PRIMES}
\section{4.5.4}
\eject % eject the previous page
\acpmark{\chd}{\csec}
\setcount0 380
\tablehead{Table 1}
\vskip 3pt
\ctrline{USEFUL PRIME NUMBERS}
\vskip 7pt
\hrule
\vskip 5pt
\baselineskip 10pt plus 1pt
\halign to size{$#\hfill$\tabskip 0pt plus 10pt
⊗\hfill#⊗\hfill#⊗\hfill#⊗\hfill#⊗\hfill#
⊗\hfill#⊗\hfill#⊗\hfill#⊗\hfill#⊗\hfill#\tabskip0pt\cr
\hfill N⊗$a↓1$⊗$a↓2$⊗$a↓3$⊗$a↓4$⊗$a↓5$⊗$a↓6$⊗$a↓7$⊗$a↓8$⊗$a↓9$⊗$a↓{10}$\cr
\noalign{\vskip 3pt}
2↑{15}⊗19⊗49⊗51⊗55⊗61⊗75⊗81⊗115⊗121⊗135\cr
2↑{16}⊗15⊗17⊗39⊗57⊗87⊗89⊗99⊗113⊗117⊗123\cr
2↑{17}⊗1⊗9⊗13⊗31⊗49⊗61⊗63⊗85⊗91⊗99\cr
2↑{18}⊗5⊗11⊗17⊗23⊗33⊗35⊗41⊗65⊗75⊗93\cr
2↑{19}⊗1⊗19⊗27⊗31⊗45⊗57⊗67⊗69⊗85⊗87\cr
2↑{20}⊗3⊗5⊗17⊗27⊗59⊗69⊗129⊗143⊗153⊗185\cr
2↑{21}⊗9⊗19⊗21⊗55⊗61⊗69⊗105⊗111⊗121⊗129\cr
2↑{22}⊗3⊗17⊗27⊗33⊗57⊗87⊗105⊗113⊗117⊗123\cr
2↑{23}⊗15⊗21⊗27⊗37⊗61⊗69⊗135⊗147⊗157⊗159\cr
2↑{24}⊗3⊗17⊗33⊗63⊗75⊗77⊗89⊗95⊗117⊗167\cr
2↑{25}⊗39⊗49⊗61⊗85⊗91⊗115⊗141⊗159⊗165⊗183\cr
2↑{26}⊗5⊗27⊗45⊗87⊗101⊗107⊗111⊗117⊗125⊗135\cr
2↑{27}⊗39⊗79⊗111⊗115⊗135⊗187⊗199⊗219⊗231⊗235\cr
2↑{28}⊗57⊗89⊗95⊗119⊗125⊗143⊗165⊗183⊗213⊗273\cr
2↑{29}⊗3⊗33⊗43⊗63⊗73⊗75⊗93⊗99⊗121⊗133\cr
2↑{30}⊗35⊗41⊗83⊗101⊗105⊗107⊗135⊗153⊗161⊗173\cr
2↑{31}⊗1⊗19⊗61⊗69⊗85⊗99⊗105⊗151⊗159⊗171\cr
2↑{32}⊗5⊗17⊗65⊗99⊗107⊗135⊗153⊗185⊗209⊗267\cr
2↑{33}⊗9⊗25⊗49⊗79⊗105⊗285⊗301⊗303⊗321⊗355\cr
2↑{34}⊗41⊗77⊗113⊗131⊗143⊗165⊗185⊗207⊗227⊗281\cr
2↑{35}⊗31⊗49⊗61⊗69⊗79⊗121⊗141⊗247⊗309⊗325\cr
2↑{36}⊗5⊗17⊗23⊗65⊗117⊗137⊗159⊗173⊗189⊗233\cr
2↑{37}⊗25⊗31⊗45⊗69⊗123⊗141⊗199⊗201⊗351⊗375\cr
2↑{38}⊗45⊗87⊗107⊗131⊗153⊗185⊗191⊗227⊗231⊗257\cr
2↑{39}⊗7⊗19⊗67⊗91⊗135⊗165⊗219⊗231⊗241⊗301\cr
2↑{40}⊗87⊗167⊗195⊗203⊗213⊗285⊗293⊗299⊗389⊗437\cr
2↑{41}⊗21⊗31⊗55⊗63⊗73⊗75⊗91⊗111⊗133⊗139\cr
2↑{42}⊗11⊗17⊗33⊗53⊗65⊗143⊗161⊗165⊗215⊗227\cr
2↑{43}⊗57⊗67⊗117⊗175⊗255⊗267⊗291⊗309⊗319⊗369\cr
2↑{44}⊗17⊗117⊗119⊗129⊗143⊗149⊗287⊗327⊗359⊗377\cr
2↑{45}⊗55⊗69⊗81⊗93⊗121⊗133⊗139⊗159⊗193⊗229\cr
2↑{46}⊗21⊗57⊗63⊗77⊗167⊗197⊗237⊗287⊗305⊗311\cr
2↑{47}⊗115⊗127⊗147⊗279⊗297⊗339⊗435⊗541⊗619⊗649\cr
2↑{48}⊗59⊗65⊗89⊗93⊗147⊗165⊗189⊗233⊗243⊗257\cr
2↑{59}⊗55⊗99⊗225⊗427⊗517⊗607⊗649⊗687⊗861⊗871\cr
2↑{60}⊗93⊗107⊗173⊗179⊗257⊗279⊗369⊗395⊗399⊗453\cr
2↑{63}⊗25⊗165⊗259⊗301⊗375⊗387⊗391⊗409⊗457⊗471\cr
2↑{64}⊗59⊗83⊗95⊗179⊗189⊗257⊗279⊗323⊗353⊗363\cr
\noalign{\vskip3pt}
10↑6⊗17⊗21⊗39⊗41⊗47⊗69⊗83⊗93⊗117⊗137\cr
10↑7⊗9⊗27⊗29⊗57⊗63⊗69⊗71⊗93⊗99⊗111\cr
10↑8⊗11⊗29⊗41⊗59⊗69⊗153⊗161⊗173⊗179⊗213\cr
10↑9⊗63⊗71⊗107⊗117⊗203⊗239⊗243⊗249⊗261⊗267\cr
10↑{10}⊗33⊗57⊗71⊗119⊗149⊗167⊗183⊗213⊗219⊗231\cr
10↑{11}⊗23⊗53⊗57⊗93⊗129⊗149⊗167⊗171⊗179⊗231\cr
10↑{12}⊗11⊗39⊗41⊗63⊗101⊗123⊗137⊗143⊗153⊗233\cr
10↑{16}⊗63⊗83⊗113⊗149⊗183⊗191⊗329⊗357⊗359⊗369\cr}
\vskip 5pt
\hrule
\vskip 5pt
\ctrline{The ten largest primes less than $N$ are $N-a↓1$, $\ldotss$, $N-a↓{10}$.}
\eject % eject previous page