Before the sanctification of the Sun of 2009, I heard rumors about the rarity of it falling out on the Passover Eve. I used my code for the Jewish calendar calculations (www.jewish-calendar.org) to list all the relevant dates and calculate the frequencies. Results were published at the time as a Google Document and are reproduced here unchanged.

From the creation of the world until the end of the sixth millennium, there are 214 cycles of the sanctification of the Sun. The dates fall from Adar 10 to Nissan 26.

Frequencies

Number of times sanctification falls on a particular day of the month are tabulated below. Turns out, only 27 days in Adar and Nissan have the sanctification of the Sun happen on them at least once. It never happens on Passover. It happens more often than on the Passover Eve on 7 days.

Day Times Histogram
Adar 10 1 *
Adar 11 0  
Adar 12 2 **
Adar 13 2 **
Adar 14 0  
Adar 15 4 **
Adar 16 0  
Adar 17 8 ****
Adar 18 0  
Adar 19 2 **
Adar 20 9 *****
Adar 21 0  
Adar 22 11 *******
Adar 23 0  
Adar 24 12 ****
Adar 25 0  
Adar 26 5 *****
Adar 27 13 *****
Adar 28 0  
Adar 29 15 *******
Nissan 1 0  
Nissan 2 19 *******
Nissan 3 0  
Nissan 4 4 **
Nissan 5 15 *******
Nissan 6 0  
Nissan 7 13 *****
Nissan 8 0  
Nissan 9 15 *******
Nissan 10 0  
Nissan 11 6 **
Nissan 12 13 *****
Nissan 13 0  
Nissan 14 12 ****
Nissan 15 0  
Nissan 16 10 ****
Nissan 17 0  
Nissan 18 3 ***
Nissan 19 8 ****
Nissan 20 0  
Nissan 21 5 *****
Nissan 22 0  
Nissan 23 5 *****
Nissan 24 0  
Nissan 25 1 *
Nissan 26 2 **

Schedule

Cycle Jewish Secular
0 1 Adar 22 -3759 February 24
1 29 Nissan 2 -3731 February 24
2 57 Adar II 12 -3703 February 24
3 85 Adar 20 -3675 February 25
4 113 Nissan 2 -3647 February 25
5 141 Adar II 10 -3619 February 25
6 169 Adar II 20 -3591 February 25
7 197 Adar 29 -3563 February 25
8 225 Nissan 9 -3535 February 25
9 253 Adar II 17 -3507 February 25
10 281 Adar 27 -3479 February 26
11 309 Nissan 9 -3451 February 26
12 337 Adar II 17 -3423 February 26
13 365 Adar 27 -3395 February 27
14 393 Nissan 7 -3367 February 27
15 421 Adar II 15 -3339 February 27
16 449 Adar 24 -3311 February 27
17 477 Nissan 5 -3283 February 28
18 505 Adar II 15 -3255 February 28
19 533 Adar 24 -3227 February 28
20 561 Nissan 5 -3199 February 28
21 589 Adar II 13 -3171 February 28
22 617 Adar 22 -3143 February 28
23 645 Nissan 2 -3115 February 28
24 673 Adar II 12 -3087 March 1
25 701 Adar II 22 -3059 March 1
26 729 Nissan 2 -3031 March 1
27 757 Nissan 12 -3003 March 1
28 785 Adar II 20 -2975 March 2
29 813 Adar 29 -2947 March 2
30 841 Nissan 9 -2919 March 2
31 869 Adar II 19 -2891 March 3
32 897 Adar 29 -2863 March 3
33 925 Nissan 9 -2835 March 3
34 953 Adar II 17 -2807 March 3
35 981 Adar 27 -2779 March 3
36 1009 Nissan 7 -2751 March 3
37 1037 Adar II 17 -2723 March 3
38 1065 Adar 26 -2695 March 4
39 1093 Nissan 5 -2667 March 4
40 1121 Adar II 15 -2639 March 4
41 1149 Adar 24 -2611 March 4
42 1177 Nissan 5 -2583 March 5
43 1205 Adar II 13 -2555 March 5
44 1233 Adar II 22 -2527 March 5
45 1261 Nissan 4 -2499 March 5
46 1289 Nissan 12 -2471 March 6
47 1317 Adar II 22 -2443 March 6
48 1345 Nissan 2 -2415 March 6
49 1373 Nissan 12 -2387 March 6
50 1401 Adar II 20 -2359 March 6
51 1429 Adar 29 -2331 March 6
52 1457 Nissan 11 -2303 March 6
53 1485 Adar II 20 -2275 March 7
54 1513 Adar 29 -2247 March 7
55 1541 Nissan 9 -2219 March 7
56 1569 Adar II 17 -2191 March 8
57 1597 Adar 27 -2163 March 8
58 1625 Nissan 7 -2135 March 8
59 1653 Adar II 17 -2107 March 8
60 1681 Adar 26 -2079 March 9
61 1709 Nissan 7 -2051 March 9
62 1737 Adar II 15 -2023 March 9
63 1765 Adar II 24 -1995 March 9
64 1793 Nissan 5 -1967 March 9
65 1821 Nissan 14 -1939 March 9
66 1849 Adar II 24 -1911 March 9
67 1877 Nissan 4 -1883 March 10
68 1905 Nissan 14 -1855 March 10
69 1933 Adar II 22 -1827 March 10
70 1961 Nissan 2 -1799 March 10
71 1989 Nissan 12 -1771 March 11
72 2017 Adar II 20 -1743 March 11
73 2045 Nissan 2 -1715 March 11
74 2073 Nissan 11 -1687 March 12
75 2101 Adar II 20 -1659 March 12
76 2129 Adar 29 -1631 March 12
77 2157 Nissan 9 -1603 March 12
78 2185 Adar II 17 -1575 March 12
79 2213 Adar 27 -1547 March 12
80 2241 Nissan 9 -1519 March 12
81 2269 Adar II 17 -1491 March 13
82 2297 Adar II 27 -1463 March 13
83 2325 Nissan 7 -1435 March 13
84 2353 Nissan 16 -1407 March 13
85 2381 Adar II 24 -1379 March 14
86 2409 Nissan 5 -1351 March 14
87 2437 Nissan 14 -1323 March 14
88 2465 Adar II 24 -1295 March 15
89 2493 Nissan 5 -1267 March 15
90 2521 Nissan 14 -1239 March 15
91 2549 Adar II 22 -1211 March 15
92 2577 Nissan 2 -1183 March 15
93 2605 Nissan 12 -1155 March 15
94 2633 Adar II 22 -1127 March 15
95 2661 Nissan 2 -1099 March 15
96 2689 Nissan 12 -1071 March 16
97 2717 Adar II 20 -1043 March 16
98 2745 Adar 29 -1015 March 16
99 2773 Nissan 9 -987 March 17
100 2801 Adar II 19 -959 March 17
101 2829 Adar II 29 -931 March 17
102 2857 Nissan 9 -903 March 17
103 2885 Nissan 18 -875 March 18
104 2913 Adar II 27 -847 March 18
105 2941 Nissan 7 -819 March 18
106 2969 Nissan 16 -791 March 18
107 2997 Adar II 26 -763 March 18
108 3025 Nissan 5 -735 March 18
109 3053 Nissan 16 -707 March 18
110 3081 Adar II 24 -679 March 19
111 3109 Nissan 5 -651 March 19
112 3137 Nissan 14 -623 March 19
113 3165 Adar II 22 -595 March 20
114 3193 Nissan 2 -567 March 20
115 3221 Nissan 12 -539 March 20
116 3249 Adar II 22 -511 March 20
117 3277 Nissan 2 -483 March 21
118 3305 Nissan 12 -455 March 21
119 3333 Adar II 20 -427 March 21
120 3361 Adar II 29 -399 March 21
121 3389 Nissan 11 -371 March 21
122 3417 Nissan 19 -343 March 21
123 3445 Adar II 29 -315 March 21
124 3473 Nissan 9 -287 March 22
125 3501 Nissan 19 -259 March 22
126 3529 Adar II 27 -231 March 22
127 3557 Nissan 7 -203 March 22
128 3585 Nissan 16 -175 March 23
129 3613 Adar II 26 -147 March 23
130 3641 Nissan 7 -119 March 23
131 3669 Nissan 16 -91 March 24
132 3697 Adar II 24 -63 March 24
133 3725 Nissan 5 -35 March 24
134 3753 Nissan 14 -7 March 24
135 3781 Adar II 24 21 March 24
136 3809 Nissan 4 49 March 24
137 3837 Nissan 14 77 March 24
138 3865 Adar II 22 105 March 25
139 3893 Nissan 2 133 March 25
140 3921 Nissan 12 161 March 25
141 3949 Nissan 21 189 March 25
142 3977 Nissan 2 217 March 26
143 4005 Nissan 11 245 March 26
144 4033 Nissan 19 273 March 26
145 4061 Adar II 29 301 March 27
146 4089 Nissan 9 329 March 27
147 4117 Nissan 19 357 March 27
148 4145 Adar II 27 385 March 27
149 4173 Nissan 7 413 March 27
150 4201 Nissan 18 441 March 27
151 4229 Adar II 27 469 March 27
152 4257 Nissan 7 497 March 27
153 4285 Nissan 16 525 March 28
154 4313 Adar II 24 553 March 28
155 4341 Nissan 5 581 March 28
156 4369 Nissan 14 609 March 29
157 4397 Adar II 24 637 March 29
158 4425 Nissan 5 665 March 29
159 4453 Nissan 14 693 March 29
160 4481 Nissan 23 721 March 30
161 4509 Nissan 2 749 March 30
162 4537 Nissan 12 777 March 30
163 4565 Nissan 21 805 March 30
164 4593 Nissan 2 833 March 30
165 4621 Nissan 11 861 March 30
166 4649 Nissan 21 889 March 30
167 4677 Adar II 29 917 March 31
168 4705 Nissan 9 945 March 31
169 4733 Nissan 19 973 March 31
170 4761 Adar II 27 1001 April 1
171 4789 Nissan 9 1029 April 1
172 4817 Nissan 18 1057 April 1
173 4845 Adar II 27 1085 April 1
174 4873 Nissan 7 1113 April 2
175 4901 Nissan 16 1141 April 2
176 4929 Adar II 26 1169 April 2
177 4957 Nissan 5 1197 April 2
178 4985 Nissan 16 1225 April 2
179 5013 Nissan 25 1253 April 2
180 5041 Nissan 5 1281 April 2
181 5069 Nissan 14 1309 April 3
182 5097 Nissan 23 1337 April 3
183 5125 Nissan 2 1365 April 3
184 5153 Nissan 12 1393 April 3
185 5181 Nissan 23 1421 April 4
186 5209 Nissan 2 1449 April 4
187 5237 Nissan 12 1477 April 4
188 5265 Nissan 21 1505 April 5
189 5293 Adar II 29 1533 April 5
190 5321 Nissan 9 1561 April 5
191 5349 Nissan 19 1589 April 5
192 5377 Adar II 29 1617 April 5
193 5405 Nissan 9 1645 April 5
194 5433 Nissan 19 1673 April 5
195 5461 Adar II 27 1701 April 6
196 5489 Nissan 7 1729 April 6
197 5517 Nissan 16 1757 April 6
198 5545 Nissan 26 1785 April 6
199 5573 Nissan 7 1813 April 7
200 5601 Nissan 16 1841 April 7
201 5629 Nissan 26 1869 April 7
202 5657 Nissan 5 1897 April 7
203 5685 Nissan 14 1925 April 8
204 5713 Nissan 23 1953 April 8
205 5741 Nissan 4 1981 April 8
206 5769 Nissan 14 2009 April 8
207 5797 Nissan 23 2037 April 8
208 5825 Nissan 2 2065 April 8
209 5853 Nissan 12 2093 April 8
210 5881 Nissan 21 2121 April 9
211 5909 Nissan 2 2149 April 9
212 5937 Nissan 11 2177 April 9
213 5965 Nissan 19 2205 April 10
214 5993 Adar II 29 2233 April 10