Block #469,097

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/31/2014, 11:28:46 PM · Difficulty 10.4313 · 6,337,405 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b097918c92ec758f281b43556ec220c47b38bbf4707eb62e9a53978d97949917

View on Chainz ↗

Height

#469,097

Difficulty

10.431282

Transactions

Size

1003 B

Version

Bits

0a6e687c

Nonce

167,547

Timestamp

3/31/2014, 11:28:46 PM

Confirmations

6,337,405

Mined by

⛏️ iAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

9c19c6c5d958783901979f19760a95eff97a2fc55dfe8b25a9f3dbd494ee36bc

Transactions (1)

Coinbase9c19c6c5d95878…f3dbd494ee36bc

1 in → 25 out9.1800 XPM913 B

AdFLJFhb…bsaVkAyh Adbb4svj…dQWTHsq5 ATp4jJhs…TbSgR8Qb AXCBfU18…vZFjKTCm AWFABhGb…QWK99PRN

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.

3.138 × 10⁹⁵(96-digit number)

31389246118857893232…30522174063629127679

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

3.138 × 10⁹⁵(96-digit number)

31389246118857893232…30522174063629127679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.277 × 10⁹⁵(96-digit number)

62778492237715786465…61044348127258255359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.255 × 10⁹⁶(97-digit number)

12555698447543157293…22088696254516510719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.511 × 10⁹⁶(97-digit number)

25111396895086314586…44177392509033021439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.022 × 10⁹⁶(97-digit number)

50222793790172629172…88354785018066042879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.004 × 10⁹⁷(98-digit number)

10044558758034525834…76709570036132085759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.008 × 10⁹⁷(98-digit number)

20089117516069051668…53419140072264171519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.017 × 10⁹⁷(98-digit number)

40178235032138103337…06838280144528343039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.035 × 10⁹⁷(98-digit number)

80356470064276206675…13676560289056686079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.607 × 10⁹⁸(99-digit number)

16071294012855241335…27353120578113372159

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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, …

Cross-reference on Chainz Explorer

Block #469,097

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