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Block #5,899

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/10/2013, 12:03:54 AM · Difficulty 7.4136 · 6,783,774 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a130e6f3bf7946af81d4d9f196df1aae99400aee3e8cec8116277f734ff766d1

View on Chainz ↗

Height

#5,899

Difficulty

7.413596

Transactions

Size

202 B

Version

Bits

0769e16b

Nonce

309

Timestamp

7/10/2013, 12:03:54 AM

Confirmations

6,783,774

Merkle Root

f441a5c72fc7e6853283108c3035be7f38ebee043fcbf9f3e6747903e4336248

Transactions (1)

Coinbasef441a5c72fc7e6…747903e4336248

1 in → 1 out18.1700 XPM108 B

AUjtw8aD…pnVP2kDr

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.

2.223 × 10¹⁰⁵(106-digit number)

22230427721555420276…19132412410758295880

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

2.223 × 10¹⁰⁵(106-digit number)

22230427721555420276…19132412410758295881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.446 × 10¹⁰⁵(106-digit number)

44460855443110840553…38264824821516591761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.892 × 10¹⁰⁵(106-digit number)

88921710886221681107…76529649643033183521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.778 × 10¹⁰⁶(107-digit number)

17784342177244336221…53059299286066367041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.556 × 10¹⁰⁶(107-digit number)

35568684354488672443…06118598572132734081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.113 × 10¹⁰⁶(107-digit number)

71137368708977344886…12237197144265468161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.422 × 10¹⁰⁷(108-digit number)

14227473741795468977…24474394288530936321

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 5899

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 a130e6f3bf7946af81d4d9f196df1aae99400aee3e8cec8116277f734ff766d1

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 #5,899 on Chainz ↗