Home/Chain Registry/Block #2,092,236

Block #2,092,236

2CCLength 12★★★★☆

Cunningham Chain of the Second Kind · Discovered 4/29/2017, 2:25:57 AM · Difficulty 10.8714 · 4,747,638 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

269dec3adf60a7648ed88fc3116dedd7966ed03017de60a158e90b408479850b

View on Chainz ↗

Height

#2,092,236

Difficulty

10.871407

Transactions

Size

61.75 KB

Version

Bits

0adf1480

Nonce

1,497,726,447

Timestamp

4/29/2017, 2:25:57 AM

Confirmations

4,747,638

Merkle Root

492d9493f543ecb2c0a0f7895ef1bd275b86fba0a7958efb63c92a9e63c5ae26

Transactions (3)

Coinbase7c12b4957bd2bb…d6874dccad5c56

1 in → 1 out9.1200 XPM110 B

AQMxF3VG…bdnjhyrL

2225acd30ecc9d…0c38b1de932234

416 in → 2 out51.7100 XPM60.21 KB

Af5eofZn…hnqGRp49 AVmNUZD7…Wz4E3T9V

5c9b76b70d0681…6ba2782cb257b5

6 in → 14 out1.8793 XPM1.34 KB

AZ3cZHxS…1qdoLqba AbsKwKHU…GqVZWvWc AXXNFpMq…JBts9TPe ASn1ZFWh…YDEgYUvG AQG4jyrV…Eu7d6GS4

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.

2.253 × 10⁹⁴(95-digit number)

22531491735692292452…49372343703091905520

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

2.253 × 10⁹⁴(95-digit number)

22531491735692292452…49372343703091905521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.506 × 10⁹⁴(95-digit number)

45062983471384584904…98744687406183811041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.012 × 10⁹⁴(95-digit number)

90125966942769169808…97489374812367622081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.802 × 10⁹⁵(96-digit number)

18025193388553833961…94978749624735244161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.605 × 10⁹⁵(96-digit number)

36050386777107667923…89957499249470488321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.210 × 10⁹⁵(96-digit number)

72100773554215335847…79914998498940976641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.442 × 10⁹⁶(97-digit number)

14420154710843067169…59829996997881953281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.884 × 10⁹⁶(97-digit number)

28840309421686134338…19659993995763906561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.768 × 10⁹⁶(97-digit number)

57680618843372268677…39319987991527813121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.153 × 10⁹⁷(98-digit number)

11536123768674453735…78639975983055626241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.307 × 10⁹⁷(98-digit number)

23072247537348907471…57279951966111252481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

4.614 × 10⁹⁷(98-digit number)

46144495074697814942…14559903932222504961

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

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 2092236

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 269dec3adf60a7648ed88fc3116dedd7966ed03017de60a158e90b408479850b

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 #2,092,236 on Chainz ↗

Block #2,092,236

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