Home/Chain Registry/Block #192

Block #192

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/7/2013, 9:24:13 PM · Difficulty 7.0043 · 6,788,802 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b426c77fc9d3e2c3ccd416338e002af6b9d79b2275e7e5991a8e82f1aadb8814

View on Chainz ↗

Height

#192

Difficulty

7.004302

Transactions

Size

206 B

Version

Bits

070119e9

Nonce

691

Timestamp

7/7/2013, 9:24:13 PM

Confirmations

6,788,802

Merkle Root

8b83702363611cbc078f8174d850838009f084ef53a7754284dabb7d05253f4b

Transactions (1)

Coinbase8b83702363611c…dabb7d05253f4b

1 in → 1 out20.3600 XPM108 B

AU8NUX9X…MYezdj53

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.

5.573 × 10¹¹⁴(115-digit number)

55737638815089438647…33423425928195567000

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

5.573 × 10¹¹⁴(115-digit number)

55737638815089438647…33423425928195566999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.114 × 10¹¹⁵(116-digit number)

11147527763017887729…66846851856391133999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.229 × 10¹¹⁵(116-digit number)

22295055526035775458…33693703712782267999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.459 × 10¹¹⁵(116-digit number)

44590111052071550917…67387407425564535999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.918 × 10¹¹⁵(116-digit number)

89180222104143101835…34774814851129071999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.783 × 10¹¹⁶(117-digit number)

17836044420828620367…69549629702258143999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.567 × 10¹¹⁶(117-digit number)

35672088841657240734…39099259404516287999

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 192

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 b426c77fc9d3e2c3ccd416338e002af6b9d79b2275e7e5991a8e82f1aadb8814

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 #192 on Chainz ↗