Home/Chain Registry/Block #521,181

Block #521,181

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/2/2014, 8:03:59 AM · Difficulty 10.8607 · 6,292,995 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6004ff5098fb844acbf2fc9bc3970fc3b247b6569695b870768b5cb92e533ffb

View on Chainz ↗

Height

#521,181

Difficulty

10.860739

Transactions

Size

878 B

Version

Bits

0adc595f

Nonce

1,021,315

Timestamp

5/2/2014, 8:03:59 AM

Confirmations

6,292,995

Merkle Root

9346ad89634555b4eab6e1e9c57e5303f87954664223898a76b0309d614be384

Transactions (4)

Coinbaseb2a1434bf6bdd8…f879f95fbe25ae

1 in → 1 out8.4900 XPM109 B

AdnhTxj2…aBbecdb8

d5acb64b64419c…b4052e074336df

1 in → 2 out7.4492 XPM226 B

APjgy8Mm…kC5BpgKE Aa145KDx…cmSzBgHB

d1bd8abec192b5…ff4d6e85a7d9c8

1 in → 2 out1.8147 XPM225 B

AG8u7ddV…cU5QJSqk AeiiADkh…qZVZPz7f

f8e5895b988581…933a2a9b4dc71d

1 in → 2 out7.4541 XPM227 B

AN3mFVC8…3JEDoVbj ALdwUwa2…9nCZi1Z6

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.

1.196 × 10⁹⁷(98-digit number)

11964985180628778055…99419419701710734400

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

1.196 × 10⁹⁷(98-digit number)

11964985180628778055…99419419701710734401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.392 × 10⁹⁷(98-digit number)

23929970361257556111…98838839403421468801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.785 × 10⁹⁷(98-digit number)

47859940722515112222…97677678806842937601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.571 × 10⁹⁷(98-digit number)

95719881445030224445…95355357613685875201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.914 × 10⁹⁸(99-digit number)

19143976289006044889…90710715227371750401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.828 × 10⁹⁸(99-digit number)

38287952578012089778…81421430454743500801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.657 × 10⁹⁸(99-digit number)

76575905156024179556…62842860909487001601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.531 × 10⁹⁹(100-digit number)

15315181031204835911…25685721818974003201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.063 × 10⁹⁹(100-digit number)

30630362062409671822…51371443637948006401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.126 × 10⁹⁹(100-digit number)

61260724124819343645…02742887275896012801

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 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

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 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 521181

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 6004ff5098fb844acbf2fc9bc3970fc3b247b6569695b870768b5cb92e533ffb

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 #521,181 on Chainz ↗

Block #521,181

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