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Block #471,779

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/2/2014, 7:49:20 PM · Difficulty 10.4355 · 6,344,619 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4e632e11adcfe7e89da363cec3b7752fe4db06a7a1feb180340cdb0a1c400153

View on Chainz ↗

Height

#471,779

Difficulty

10.435463

Transactions

Size

4.09 KB

Version

Bits

0a6f7a88

Nonce

5,000

Timestamp

4/2/2014, 7:49:20 PM

Confirmations

6,344,619

Merkle Root

c472de66c5c2f7700dbce6b697c3157cc08a01edb6cc4dae8d8e27a3d9cfe0f1

Transactions (4)

Coinbase85e2e298430320…36fd48c6260f8b

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

b84f707e7a68fe…804d006f352b69

5 in → 12 out38.1525 XPM1023 B

AVLbPnVT…MXTBm469 AYnmeXDa…i6iyxrbi AYt6BJ6b…FyxD6rgv AJGng3Vu…HfiEdb5C AeKNrjNj…1NEq95Ta

7b4a17090cbae2…e76e7a3aaf7400

17 in → 2 out32.1160 XPM2.53 KB

AeZwJAt8…ZVEjFh8b AG9aVVAX…qBR7Y3pA

74bb18f724121b…de71333eec76da

2 in → 2 out3.0722 XPM374 B

AXDS5S83…LHa58BH1 AY7LWjoJ…VLfFyyVA

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.

6.024 × 10¹⁰⁰(101-digit number)

60249928532021539931…02110182614461562960

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

6.024 × 10¹⁰⁰(101-digit number)

60249928532021539931…02110182614461562961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.204 × 10¹⁰¹(102-digit number)

12049985706404307986…04220365228923125921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.409 × 10¹⁰¹(102-digit number)

24099971412808615972…08440730457846251841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.819 × 10¹⁰¹(102-digit number)

48199942825617231945…16881460915692503681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.639 × 10¹⁰¹(102-digit number)

96399885651234463890…33762921831385007361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.927 × 10¹⁰²(103-digit number)

19279977130246892778…67525843662770014721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.855 × 10¹⁰²(103-digit number)

38559954260493785556…35051687325540029441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.711 × 10¹⁰²(103-digit number)

77119908520987571112…70103374651080058881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.542 × 10¹⁰³(104-digit number)

15423981704197514222…40206749302160117761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.084 × 10¹⁰³(104-digit number)

30847963408395028444…80413498604320235521

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 471779

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 4e632e11adcfe7e89da363cec3b7752fe4db06a7a1feb180340cdb0a1c400153

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 #471,779 on Chainz ↗

Block #471,779

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