Home/Chain Registry/Block #8,003

Block #8,003

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/10/2013, 1:33:10 PM · Difficulty 7.5465 · 6,781,159 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7570d4990326be5952c13fae6826d6e45ec0322c9d8fa95ed2e220e5c5764975

View on Chainz ↗

Height

#8,003

Difficulty

7.546501

Transactions

Size

205 B

Version

Bits

078be780

Nonce

127

Timestamp

7/10/2013, 1:33:10 PM

Confirmations

6,781,159

Merkle Root

96763e6850181c6b5511961b56310e449ae52e8e1de3eae2651cf94f97d2e076

Transactions (1)

Coinbase96763e6850181c…1cf94f97d2e076

1 in → 1 out17.5400 XPM108 B

AKe9SqoD…a7UiZnEY

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.

1.109 × 10¹¹¹(112-digit number)

11090769482307416441…53923082968308461360

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

1.109 × 10¹¹¹(112-digit number)

11090769482307416441…53923082968308461359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.218 × 10¹¹¹(112-digit number)

22181538964614832882…07846165936616922719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.436 × 10¹¹¹(112-digit number)

44363077929229665764…15692331873233845439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.872 × 10¹¹¹(112-digit number)

88726155858459331529…31384663746467690879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.774 × 10¹¹²(113-digit number)

17745231171691866305…62769327492935381759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.549 × 10¹¹²(113-digit number)

35490462343383732611…25538654985870763519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.098 × 10¹¹²(113-digit number)

70980924686767465223…51077309971741527039

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 8003

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 7570d4990326be5952c13fae6826d6e45ec0322c9d8fa95ed2e220e5c5764975

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 #8,003 on Chainz ↗