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.

1.558 × 10⁹⁸(99-digit number)

15580477091290325522…35379007905120256000

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

1.558 × 10⁹⁸(99-digit number)

15580477091290325522…35379007905120256001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.116 × 10⁹⁸(99-digit number)

31160954182580651044…70758015810240512001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.232 × 10⁹⁸(99-digit number)

62321908365161302089…41516031620481024001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.246 × 10⁹⁹(100-digit number)

12464381673032260417…83032063240962048001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.492 × 10⁹⁹(100-digit number)

24928763346064520835…66064126481924096001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.985 × 10⁹⁹(100-digit number)

49857526692129041671…32128252963848192001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.971 × 10⁹⁹(100-digit number)

99715053384258083342…64256505927696384001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.994 × 10¹⁰⁰(101-digit number)

19943010676851616668…28513011855392768001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.988 × 10¹⁰⁰(101-digit number)

39886021353703233336…57026023710785536001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.977 × 10¹⁰⁰(101-digit number)

79772042707406466673…14052047421571072001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.595 × 10¹⁰¹(102-digit number)

15954408541481293334…28104094843142144001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

3.190 × 10¹⁰¹(102-digit number)

31908817082962586669…56208189686284288001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second 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

ExceptionalChain length 12

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 2CC formula:

2CC: 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 851022

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 247526aa5360aa60557001c0ec0269e706797695a38aeebd1226af59a7e2d57b

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 #851,022 on Chainz ↗

Block #851,022

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