Home/Chain Registry/Block #757

Block #757

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/8/2013, 4:05:00 AM · Difficulty 7.0361 · 6,788,315 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2fc07d877866a210a02f684eab6a4251534b1e367f0dbf7fd3683b7b47db7637

View on Chainz ↗

Height

#757

Difficulty

7.036137

Transactions

Size

199 B

Version

Bits

0709404e

Nonce

Timestamp

7/8/2013, 4:05:00 AM

Confirmations

6,788,315

Merkle Root

a7d915dd3ea1747636576d5dabc46cc5e2b9d72a4e6b32f4fb806c6e07a38cce

Transactions (1)

Coinbasea7d915dd3ea174…806c6e07a38cce

1 in → 1 out20.1700 XPM108 B

AYiMok1N…YrvNJhHb

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.

5.791 × 10⁹⁷(98-digit number)

57914692304792647505…51292179299716844000

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

5.791 × 10⁹⁷(98-digit number)

57914692304792647505…51292179299716844001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.158 × 10⁹⁸(99-digit number)

11582938460958529501…02584358599433688001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.316 × 10⁹⁸(99-digit number)

23165876921917059002…05168717198867376001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.633 × 10⁹⁸(99-digit number)

46331753843834118004…10337434397734752001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.266 × 10⁹⁸(99-digit number)

92663507687668236009…20674868795469504001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.853 × 10⁹⁹(100-digit number)

18532701537533647201…41349737590939008001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.706 × 10⁹⁹(100-digit number)

37065403075067294403…82699475181878016001

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 757

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 2fc07d877866a210a02f684eab6a4251534b1e367f0dbf7fd3683b7b47db7637

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 #757 on Chainz ↗