Home/Chain Registry/Block #85,098

Block #85,098

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/27/2013, 5:45:45 AM · Difficulty 9.2835 · 6,709,177 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

097e011d67a091b9f85aa72313da9fd658401ae9c29db1183fa610eaaca1897d

View on Chainz ↗

Height

#85,098

Difficulty

9.283468

Transactions

Size

211 B

Version

Bits

09489159

Nonce

553

Timestamp

7/27/2013, 5:45:45 AM

Confirmations

6,709,177

Merkle Root

58259d1bba9321afbc1088c7be6ba75dea20825a14dc6ec0c0aa919fbb9f915c

Transactions (1)

Coinbase58259d1bba9321…aa919fbb9f915c

1 in → 1 out11.5900 XPM110 B

ALgWhQmp…kyQ4FJ9M

Prime Chain Origin

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.

9.853 × 10¹¹⁹(120-digit number)

98536501794988425826…12322915509187880650

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

9.853 × 10¹¹⁹(120-digit number)

98536501794988425826…12322915509187880651

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.970 × 10¹²⁰(121-digit number)

19707300358997685165…24645831018375761301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.941 × 10¹²⁰(121-digit number)

39414600717995370330…49291662036751522601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.882 × 10¹²⁰(121-digit number)

78829201435990740661…98583324073503045201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.576 × 10¹²¹(122-digit number)

15765840287198148132…97166648147006090401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.153 × 10¹²¹(122-digit number)

31531680574396296264…94333296294012180801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.306 × 10¹²¹(122-digit number)

63063361148792592528…88666592588024361601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.261 × 10¹²²(123-digit number)

12612672229758518505…77333185176048723201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.522 × 10¹²²(123-digit number)

25225344459517037011…54666370352097446401

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 85098

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 097e011d67a091b9f85aa72313da9fd658401ae9c29db1183fa610eaaca1897d

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 #85,098 on Chainz ↗