Home/Chain Registry/Block #251,758

Block #251,758

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/9/2013, 5:04:56 AM · Difficulty 9.9703 · 6,543,183 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ab32e00a8994c17b7c1ba91d544e880794b41e6fe2314758f8e0a16f3b1eb624

View on Chainz ↗

Height

#251,758

Difficulty

9.970268

Transactions

Size

1.09 KB

Version

Bits

09f86379

Nonce

41,394

Timestamp

11/9/2013, 5:04:56 AM

Confirmations

6,543,183

Merkle Root

5da97add6810b908072d40a575cb70df57a9910a2686d8f6cdf8196520149c63

Transactions (4)

Coinbasea0f0c1889e7bb3…effea746847746

1 in → 1 out10.0700 XPM109 B

AdBW7org…oaQ1XT7w

076b783d9a62b8…a76d103d92ebbd

1 in → 4 out29.9900 XPM294 B

AeXd5LCA…sbQkRqrm AZKgQwBY…rTXiwBnJ ASgyYipS…fmDqzxmT AKSzcsCn…E7LqFQdb

1cc285eb30a3ca…fb17a392db6d56

1 in → 5 out20.4342 XPM328 B

AGpXx9rf…iHvnNyjV Acsv2pk5…hmtFjoTQ AaXk8q9Y…CRNFL9rW AeXd5LCA…sbQkRqrm AHA3zt1m…D9PJyKHt

b4dfcd75dbef58…2688ef24020804

1 in → 4 out12.4242 XPM295 B

AWc8Xa3G…VUP6LJar AHA3zt1m…D9PJyKHt AZKgQwBY…rTXiwBnJ ASgyYipS…fmDqzxmT

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.

4.703 × 10⁹³(94-digit number)

47030808243019505604…51248104060545641040

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

4.703 × 10⁹³(94-digit number)

47030808243019505604…51248104060545641041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.406 × 10⁹³(94-digit number)

94061616486039011208…02496208121091282081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.881 × 10⁹⁴(95-digit number)

18812323297207802241…04992416242182564161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.762 × 10⁹⁴(95-digit number)

37624646594415604483…09984832484365128321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.524 × 10⁹⁴(95-digit number)

75249293188831208966…19969664968730256641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.504 × 10⁹⁵(96-digit number)

15049858637766241793…39939329937460513281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.009 × 10⁹⁵(96-digit number)

30099717275532483586…79878659874921026561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.019 × 10⁹⁵(96-digit number)

60199434551064967173…59757319749842053121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.203 × 10⁹⁶(97-digit number)

12039886910212993434…19514639499684106241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.407 × 10⁹⁶(97-digit number)

24079773820425986869…39029278999368212481

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 251758

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 ab32e00a8994c17b7c1ba91d544e880794b41e6fe2314758f8e0a16f3b1eb624

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 #251,758 on Chainz ↗