Home/Chain Registry/Block #167,424

Block #167,424

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/16/2013, 2:23:48 PM · Difficulty 9.8686 · 6,649,600 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

feecb008bb63bd766f2f3ababa89ba046747de4e36c6325038959d4c598ced02

View on Chainz ↗

Height

#167,424

Difficulty

9.868569

Transactions

Size

1.76 KB

Version

Bits

09de5a8a

Nonce

135,826

Timestamp

9/16/2013, 2:23:48 PM

Confirmations

6,649,600

Merkle Root

2efd176cc47b42a765403e11c8d4f82900f3dae1bd920bd0a1c664993035d43e

Transactions (4)

Coinbaseb4d6ff920129c8…b10086376ebce1

1 in → 1 out10.2800 XPM109 B

ANB7PfrL…CNt513wc

e8ca58cd8cd7a6…a2b868577f022c

3 in → 2 out0.2000 XPM521 B

APDEimvp…7nmdzk8D AKV7FaeB…SvBG6FUV

48771b603706ea…14902a314d9043

3 in → 2 out0.2000 XPM524 B

APDEimvp…7nmdzk8D AFzHfDjr…68sZFcb3

98c97ba808f130…a21da4d13f2791

3 in → 3 out0.2304 XPM557 B

AWcZjGw7…FWC6X8Wu ASAsGHv7…HmwPgi2n AZKDPwuc…J9BTHV94

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.

2.351 × 10⁹⁴(95-digit number)

23513960142294285123…10748019153422050400

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

2.351 × 10⁹⁴(95-digit number)

23513960142294285123…10748019153422050399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.702 × 10⁹⁴(95-digit number)

47027920284588570246…21496038306844100799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.405 × 10⁹⁴(95-digit number)

94055840569177140492…42992076613688201599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.881 × 10⁹⁵(96-digit number)

18811168113835428098…85984153227376403199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.762 × 10⁹⁵(96-digit number)

37622336227670856196…71968306454752806399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.524 × 10⁹⁵(96-digit number)

75244672455341712393…43936612909505612799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.504 × 10⁹⁶(97-digit number)

15048934491068342478…87873225819011225599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.009 × 10⁹⁶(97-digit number)

30097868982136684957…75746451638022451199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.019 × 10⁹⁶(97-digit number)

60195737964273369915…51492903276044902399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.203 × 10⁹⁷(98-digit number)

12039147592854673983…02985806552089804799

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 First 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 1CC formula:

1CC: 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 167424

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 feecb008bb63bd766f2f3ababa89ba046747de4e36c6325038959d4c598ced02

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 #167,424 on Chainz ↗

Block #167,424

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