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Block #512

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/8/2013, 1:21:38 AM · Difficulty 7.0206 · 6,788,473 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7858eef6eb2e0f157f8e3f2fc0fea1cefa988c63452e877dccb5c8f5e1c89db6

View on Chainz ↗

Height

#512

Difficulty

7.020575

Transactions

Size

202 B

Version

Bits

0705446c

Nonce

Timestamp

7/8/2013, 1:21:38 AM

Confirmations

6,788,473

Merkle Root

e7c2c6dab70bb89bbee4ead556a47d712848bc53817617f1265151baa2afa1d3

Transactions (1)

Coinbasee7c2c6dab70bb8…5151baa2afa1d3

1 in → 1 out20.2600 XPM108 B

AdV5Vw5N…owsi9s2P

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.

2.019 × 10¹⁰⁵(106-digit number)

20190654253808031759…29629331523440168950

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

2.019 × 10¹⁰⁵(106-digit number)

20190654253808031759…29629331523440168949

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.038 × 10¹⁰⁵(106-digit number)

40381308507616063518…59258663046880337899

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.076 × 10¹⁰⁵(106-digit number)

80762617015232127036…18517326093760675799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.615 × 10¹⁰⁶(107-digit number)

16152523403046425407…37034652187521351599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.230 × 10¹⁰⁶(107-digit number)

32305046806092850814…74069304375042703199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.461 × 10¹⁰⁶(107-digit number)

64610093612185701629…48138608750085406399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.292 × 10¹⁰⁷(108-digit number)

12922018722437140325…96277217500170812799

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 First 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 1CC formula:

1CC: 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 512

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 7858eef6eb2e0f157f8e3f2fc0fea1cefa988c63452e877dccb5c8f5e1c89db6

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 #512 on Chainz ↗