Geodesic
Calculation of random pairs of primes whose product lies in a given short interval
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 150-154.

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The paper proposes heuristic algorithms for constructing pairs of random primes, the product of which lies in a given interval $ \left (\Delta, \, \Delta + \delta \right). $ One algorithm refers to the case $ \delta = \sqrt {\Delta }, $ and the second to $ \delta = 30 \Delta^{1/3}. $ They allow in the well-known RSA cryptosystem to choose shorter public keys (twice for the first algorithm and three times for the second). 
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V. A. Bykovskii. Calculation of random pairs of primes whose product lies in a given short interval. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 150-154. http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a3/

[1] Rivest R. L., Shamir A., Adleman L., “Method for Obtaining Digital Signatures and Public-Key Cryptosystems”, Commun. ACM, 21:2 (1978), 120–126 | DOI | MR | Zbl

[2] Hyxley M. N., “On the difference between consecutive primes”, Invent. math., 15 (1972), 164–170 | DOI | MR