Home/Chain Registry/Block #513

Block #513

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/8/2013, 1:21:54 AM · Difficulty 7.0205 · 6,788,466 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b36383a94fcae784cc0daf95df3718f0c376c603e72e3749f7973733e8af1008

View on Chainz ↗

Height

#513

Difficulty

7.020491

Transactions

Size

199 B

Version

Bits

07053ee8

Nonce

515

Timestamp

7/8/2013, 1:21:54 AM

Confirmations

6,788,466

Merkle Root

b8defc07417a57ff04229dda622c349cc783979dbf34182c2170ea87bdca2017

Transactions (1)

Coinbaseb8defc07417a57…70ea87bdca2017

1 in → 1 out20.2600 XPM108 B

AT19KRPw…TtRQStTF

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.

2.934 × 10⁹⁷(98-digit number)

29343833249567860973…24277508521466069300

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

2.934 × 10⁹⁷(98-digit number)

29343833249567860973…24277508521466069301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.868 × 10⁹⁷(98-digit number)

58687666499135721946…48555017042932138601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.173 × 10⁹⁸(99-digit number)

11737533299827144389…97110034085864277201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.347 × 10⁹⁸(99-digit number)

23475066599654288778…94220068171728554401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.695 × 10⁹⁸(99-digit number)

46950133199308577557…88440136343457108801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.390 × 10⁹⁸(99-digit number)

93900266398617155114…76880272686914217601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.878 × 10⁹⁹(100-digit number)

18780053279723431022…53760545373828435201

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 513

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 b36383a94fcae784cc0daf95df3718f0c376c603e72e3749f7973733e8af1008

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 #513 on Chainz ↗