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# Piece: https://leibnizlegible.com/api/records/27899/text
# Catalogue record: 27899 — Numeri primi eorumque genesis mira
# Incipit: ab_2c+d[...]N est numerus primus
# Date: 1677-09-16 (77-09-06)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=27899&katnr=57017
# Work: https://leibnizlegible.com/work/00068014
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 17
# Folios: Bl. 1 (from the shelfmark LH 35, 4, 17 Bl. 1): 2 pages, canvases 1–2, page ids 00068014:0001 to 00068014:0002
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068014&page=1
# Lines: 105 recognised on 2 of 2 pages, mean confidence 0.88
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 1r — 00068014:0001
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068014/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 80 lines, status machine
Numeri primi eorum genesis mira
abc + d 5 N. est numerus
primus integer modo in a. b. c. d.
numeri primi dat N. radice quadra
minores.
1+ , 1+.
92, +, 12+
12, +5 1 +1+
323, , = 1 123, +
n 133,  A 12, + 1, 2 + 1 1 6+2 + 2 + 1 12,3, + 5) vu det 
+ 1,2,3, + 1
16+6+ 1 1,23, +7 (12
+ 1, 23, + 1,2, +1, 2, + 1(,6+6 +2+2 + 1) 12,3, +11)
6+ 6 +6+ + 1
1,23, 135
6+6+6 + 2 + 2 + 1 ( 1,2131 17C
257. (5 = 16+6 +6+6 + 1
6+6,66 + 2 + 2 +
30 + 1
30 +6+ 1
30 +6+ 2+ 2 + 1
30 +6+6+ 1
30 +6+61Z +2 +1 
30 +6 +6+6 + 1
30 +6+6+6 +8+2 +2-
Hi omne componuntur
ex numelis interi primis
in
30+ 6+6+6 +6 +2 +2 +1
Septem
A,2 
d, 213, a B
133) (2,19) 
caacetiou
(43.) (11, 13) 
a 17
+iga 169
+143 1t2
+149 170
semper quilibet gradus ita praecise finori
satet, ubi nuus primus superet qui amplius addi possit
1, 273 
69 19
1. 23, en 1F. 12, 5, +3, 1315 +2
213,51, +1
3 1
oncta
aatica
quae numeros primos referunt, omnesque continent primos sati numeri
quadralica
ax Datus numerus an primu sit non melius sciri potest, quam si ita resolvatur
radice minores
ut omnes numeri primi minores radice compositionem ejus ingrediantur
151. etus radixe minores numeri primi usque ad 11. inclusive. 12,3, 5C 130. et 7, 11 p77
Ergo 151+ 1,2, 3, 5,, + 2,11, + 1,2,3, +2 qui numerus dividi non pt
per per 2.
2,11, +25 79 quiest prim 103
1 nec per ultum altum ob 3 quo 7, 11,, +2. non est divisile t +TN30+14
a nec ob similes rationes per 5, quia b +c Ad non est divisile per 5, nec por 7 Z 2,6+
 a + c +d non est divisile per 7. sed optimum foret unum quemque numerum
desolvere in primos radice minores, ut unus quisque iumerctum exter in primorum extet
in omnibus terminis praeter quam in uno, ut ab C + abd + Vdd est necessario pitam
si ab. a. b. c. sint omnes termini primi ejus radic  minores, id est numorus ipse diber esse inter q er4
nempe ap eg. 5 h1. 43. ∞
potest et quiliber tertuinus per quemlibet alium numerm mulliplocar
12A 5,, + 1, 2st,
non potest componi affirmatiae
ex 1,2
iudice quadralica dati non
79 id est 30 + 49 est num erus primus
10725
10l 30+771107
H9) (712)
10 2129.. 100
45... . .. 11
et tamen hic omisolis. Ergo
Tabula sic nec omnes ex hiberet
100+2, 2, 5,5
90000013, 2,5
103 193

## Folio 1v — 00068014:0002
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068014/jpgs/default/00000002.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 25 lines, status machine
itaque scribi potent
abc infinitae varietates
asito Q essi
pro mutatione literarum et potestatum quae inter e id utile esset affirmando negandoque ad componen
dum datum numerum pumum jungi possent. N si vero a. b. c. d sunt ofunc
sunt 2 3 5 7
Ese numems primus datus erit inter 49 et 121, qui sic componendus est ut indivisibilitas
apparent ex terminis. Nota si Z valet debent S. +. v. X esse 0. et contra, si
volumus ut ex expressione hac analytica apparent indivosibilitas
an addi possunt: ab + ac + ad + bc + bd + cd Tulis quantitas etium non potest
dividi nec per a ob bc +bd + cd nec per aliam ob timilem rationem. Item si
aliquae abessent taman non posset dividi, ut auferarau ab, vel etiam ab + ac
itaque varii numeri sex vel quatuor partium indefieri possunt omnes primi
et à se invicen diferentes
Regula autem a sola formuta, non vero a consideratione, u omnes
primi rudice minores contineantur dependens c(quia virtate id inde sequitur
sponte) haec est, u sint primi omnes deinces, ab unitate post  unitate
abcd fieut inde abed abe ab bcd+
1 + abcd a + bcd) b + acd) c + abd) d + abc
211
a b + cd
107
ac + bd) ad + bc
Hic jam displicet quod redit 31
quod jam fuelat