數論上,如果將所有質數寫出,然後計算出相鄰數的差,得出一個新的數列,又再計算新數列相鄰數的差,重複這個動作無限次:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
1, 2, 2, 4, 2, 4, 2, 4, 6, 2, ...
1, 0, 2, 2, 2, 2, 2, 2, 4, ...
1, 2, 0, 0, 0, 0, 0, 2, ...
1, 2, 0, 0, 0, 0, 2, ...
1, 2, 0, 0, 0, 2, ...
1, 2, 0, 0, 2, ...

吉爾布雷斯猜想猜測除了原本質數數列之外,這些數列的首個數都是1,在1958年由Norman O. Gilbreath提出。

更數學化來說,將定義為第個質數,,其中是非負整數,是正整數。證明對於所有正整數

1993年,安德魯·歐德里茲科檢查了以下的質數(346,065,536,839行),都符合此猜想。(相關論文為Iterated absolute values of differences of consecutive primes,可在[1]頁面存檔備份,存於網際網路檔案館)下載。)

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