RandomSafePrime

Compute one or more safe primes in a requested range

ResourceFunction["RandomSafePrime"][max]

gives a safe prime equal or less than max.

ResourceFunction["RandomSafePrime"][{min,max}]

gives a safe prime in the range min to max.

ResourceFunction["RandomSafePrime"][range,n]

gives n safe primes in the specified range.

Details and Options

ResourceFunction["RandomSafePrime"] uses RandomPrime to generate candidate safe primes. Generating the requested number of safe primes may take a significant amount of time. Ranges which contain no safe primes will eventually time out.

RandomSafePrime will time out after 60 seconds. This time-out can be modfied with the TimeConstraint option.

Examples

Basic Examples

Generate a random safe prime:

In[1]:=

$p = ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/\ Function/RandomSafePrime"][2^64]$

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Check that it is indeed a safe prime:

In[2]:=

$ResourceFunction[ ResourceObject[ Association[ "Name" -> "SafePrimeQ", "ShortName" -> "SafePrimeQ", "UUID" -> "771122ee-cbcc-4893-a2f9-dc488d210486", "ResourceType" -> "Function", "Version" -> "1.0.0", "Description" -> "Determine whether a number is a safe prime", "RepositoryLocation" -> URL[ "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"], "SymbolName" -> "FunctionRepository`$\ 9e23b991252c4411863be568f6325ac8`SafePrimeQ", "FunctionLocation" -> CloudObject[ "https://www.wolframcloud.com/obj/8a5611ea-4462-4a67-a3ce-\ 052cce5b4c60"]], ResourceSystemBase -> Automatic]][p]$

Out[2]=

Generate several safe primes:

In[3]:=

$list = ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/\ Function/RandomSafePrime"][2^64, 10]$

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Check that they are safe primes:

In[4]:=

$Map[ResourceFunction[ ResourceObject[ Association[ "Name" -> "SafePrimeQ", "ShortName" -> "SafePrimeQ", "UUID" -> "771122ee-cbcc-4893-a2f9-dc488d210486", "ResourceType" -> "Function", "Version" -> "1.0.0", "Description" -> "Determine whether a number is a safe prime", "RepositoryLocation" -> URL[ "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"], "SymbolName" -> "FunctionRepository`$\ 9e23b991252c4411863be568f6325ac8`SafePrimeQ", "FunctionLocation" -> CloudObject[ "https://www.wolframcloud.com/obj/8a5611ea-4462-4a67-a3ce-\ 052cce5b4c60"]], ResourceSystemBase -> Automatic]], list]$

Out[4]=

Scope

Generate a safe prime in a specific range:

In[5]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/Function/\ RandomSafePrime"][{1000, 2000}]$

Out[5]=

Generate several safe primes in a specific range:

In[6]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/Function/\ RandomSafePrime"][{1000, 2000}, 10]$

Out[6]=

Options

Attempting to generate a large number of safe primes in a small amount of time will time out:

In[7]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/Function/\ RandomSafePrime"][{2^32, 2^40}, 10000, TimeConstraint -> 1]$

Out[7]=