This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.833 × 10⁹⁴(95-digit number)

98330480062640632751…19492546323662092340

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

9.833 × 10⁹⁴(95-digit number)

98330480062640632751…19492546323662092339

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.966 × 10⁹⁵(96-digit number)

19666096012528126550…38985092647324184679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.933 × 10⁹⁵(96-digit number)

39332192025056253100…77970185294648369359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.866 × 10⁹⁵(96-digit number)

78664384050112506200…55940370589296738719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.573 × 10⁹⁶(97-digit number)

15732876810022501240…11880741178593477439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.146 × 10⁹⁶(97-digit number)

31465753620045002480…23761482357186954879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.293 × 10⁹⁶(97-digit number)

62931507240090004960…47522964714373909759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.258 × 10⁹⁷(98-digit number)

12586301448018000992…95045929428747819519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.517 × 10⁹⁷(98-digit number)

25172602896036001984…90091858857495639039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.034 × 10⁹⁷(98-digit number)

50345205792072003968…80183717714991278079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 291846

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock ba137ec70acbafb7f8e81ead6a0e777442dc786f475ab456eef546b0a21d01ec

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #291,846 on Chainz ↗

Block #291,846

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