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Block #547,719

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/16/2014, 3:31:42 PM · Difficulty 10.9576 · 6,278,979 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9ed092e84905de5eb0a39bf6f54e8e3fd052bb78e298d8d02e453b727f0fb254

View on Chainz ↗

Height

#547,719

Difficulty

10.957586

Transactions

Size

658 B

Version

Bits

0af52460

Nonce

120,787,692

Timestamp

5/16/2014, 3:31:42 PM

Confirmations

6,278,979

Merkle Root

33aa21ddeeecc919137f369d394385c731a712ae53f12c4bc7f4aa8aff2dab2c

Transactions (3)

Coinbase2c8c8c3ee20a0e…cae1166d860bf2

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

e6ee9a9148c9f7…67aef196abce11

1 in → 2 out16.9791 XPM226 B

AKRMruR3…hH8RzC4Z ALPnRfZa…j9uummgi

711be3ea04189a…ee3a804ccb8876

1 in → 2 out38.6768 XPM225 B

AVkR7Akb…gDKoKHLb ATWZTH6n…1jakkyRe

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.

6.144 × 10⁹⁷(98-digit number)

61443079570937850423…62371566893681091740

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

6.144 × 10⁹⁷(98-digit number)

61443079570937850423…62371566893681091741

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.228 × 10⁹⁸(99-digit number)

12288615914187570084…24743133787362183481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.457 × 10⁹⁸(99-digit number)

24577231828375140169…49486267574724366961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.915 × 10⁹⁸(99-digit number)

49154463656750280338…98972535149448733921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.830 × 10⁹⁸(99-digit number)

98308927313500560677…97945070298897467841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.966 × 10⁹⁹(100-digit number)

19661785462700112135…95890140597794935681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.932 × 10⁹⁹(100-digit number)

39323570925400224271…91780281195589871361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.864 × 10⁹⁹(100-digit number)

78647141850800448542…83560562391179742721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.572 × 10¹⁰⁰(101-digit number)

15729428370160089708…67121124782359485441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.145 × 10¹⁰⁰(101-digit number)

31458856740320179416…34242249564718970881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

6.291 × 10¹⁰⁰(101-digit number)

62917713480640358833…68484499129437941761

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 547719

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 9ed092e84905de5eb0a39bf6f54e8e3fd052bb78e298d8d02e453b727f0fb254

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 #547,719 on Chainz ↗

Block #547,719

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