Home/Chain Registry/Block #5,898

Block #5,898

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/10/2013, 12:03:37 AM · Difficulty 7.4135 · 6,783,674 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

396288159c90dd4b1410040989de265d6fa3b3115baae38c5a8c4eee1d827318

View on Chainz ↗

Height

#5,898

Difficulty

7.413549

Transactions

Size

199 B

Version

Bits

0769de5e

Nonce

238

Timestamp

7/10/2013, 12:03:37 AM

Confirmations

6,783,674

Merkle Root

1ca16050151723079a79768e772d1fa8323316e3d29bb0592ac2ba7dcba170aa

Transactions (1)

Coinbase1ca16050151723…c2ba7dcba170aa

1 in → 1 out18.1700 XPM108 B

AXLtYaJU…YKXxkHiA

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.

2.523 × 10⁹⁸(99-digit number)

25236033240632561005…76795927658036115200

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

2.523 × 10⁹⁸(99-digit number)

25236033240632561005…76795927658036115201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.047 × 10⁹⁸(99-digit number)

50472066481265122011…53591855316072230401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.009 × 10⁹⁹(100-digit number)

10094413296253024402…07183710632144460801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.018 × 10⁹⁹(100-digit number)

20188826592506048804…14367421264288921601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.037 × 10⁹⁹(100-digit number)

40377653185012097608…28734842528577843201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.075 × 10⁹⁹(100-digit number)

80755306370024195217…57469685057155686401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.615 × 10¹⁰⁰(101-digit number)

16151061274004839043…14939370114311372801

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 5898

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 396288159c90dd4b1410040989de265d6fa3b3115baae38c5a8c4eee1d827318

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 #5,898 on Chainz ↗