Home/Chain Registry/Block #184,991

Block #184,991

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/29/2013, 12:04:11 AM · Difficulty 9.8621 · 6,609,154 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

06ae38b47aae2d6d8f7e7eb94ebbe7463fef8d51ebe9b8a2f21b05f254e58f9f

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Height

#184,991

Difficulty

9.862056

Transactions

Size

196 B

Version

Bits

09dcafb7

Nonce

120,592

Timestamp

9/29/2013, 12:04:11 AM

Confirmations

6,609,154

Merkle Root

cedb1a0b424bba94d3a33dd47de0ca36c43712910fb08bbf246b25d11c8de1b1

Transactions (1)

Coinbasecedb1a0b424bba…6b25d11c8de1b1

1 in → 1 out10.2700 XPM109 B

Aah59eDE…Nny9AgXr

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.

6.173 × 10⁸⁷(88-digit number)

61737601215294883608…04626406828847109040

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

6.173 × 10⁸⁷(88-digit number)

61737601215294883608…04626406828847109041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.234 × 10⁸⁸(89-digit number)

12347520243058976721…09252813657694218081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.469 × 10⁸⁸(89-digit number)

24695040486117953443…18505627315388436161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.939 × 10⁸⁸(89-digit number)

49390080972235906886…37011254630776872321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.878 × 10⁸⁸(89-digit number)

98780161944471813773…74022509261553744641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.975 × 10⁸⁹(90-digit number)

19756032388894362754…48045018523107489281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.951 × 10⁸⁹(90-digit number)

39512064777788725509…96090037046214978561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.902 × 10⁸⁹(90-digit number)

79024129555577451018…92180074092429957121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.580 × 10⁹⁰(91-digit number)

15804825911115490203…84360148184859914241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.160 × 10⁹⁰(91-digit number)

31609651822230980407…68720296369719828481

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 184991

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 06ae38b47aae2d6d8f7e7eb94ebbe7463fef8d51ebe9b8a2f21b05f254e58f9f

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 #184,991 on Chainz ↗