Christianity has consistently condemned numerology,1 a broad term that includes arithmancy,2 since the earliest times. This false belief comes from the reality that God has used numbers to convey real meaning.3 The difference is that this meaning is in no way "magical" or intended to tell us about future events, it rather tells us about the nature of reality as it currently exists.
Mrs. Rowling, in writing her series, has clearly drawn ideas from the Christian (and Jewish) understanding of significant numbers. Thus understanding the significance of numbers like three or seven can help understand the books better.
Thus I expect that in Rowling's universe, the following numbers would be "magically powerful":
- three - a lesser (than seven) completeness.
- seven - both physical and spiritual perfection
- nine - complete finality
- ten - law, responsibility and complete order
- twelve - divine power and authority
- seventeen - complete victory over an enemy
- nineteen - perfect order/perfect judgement
- twenty - perfect waiting period
- thirty-three - promises kept
Footnotes
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Mr. Jake Ashcraft. "What Is the Significance of Biblical Numerology?" Published 2021-04-15. Christianity.com. ↩
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Wikipedia "Arithmancy" Last Edited: 2022-07-26. Last Viewed: 2022-07-28. ↩
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Bible Study. "Meaning of Numbers in the Bible" Last Viewed: 2022-07-28. ↩