Block #448,311

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 8:11:12 PM · Difficulty 10.3678 · 6,368,857 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a4100c0fd207bfb7a5e268ccca0c010dc0ef0b8c408fb97f526b27428a8695a3

View on Chainz ↗

Height

#448,311

Difficulty

10.367820

Transactions

Size

205 B

Version

Bits

0a5e296e

Nonce

42,039

Timestamp

3/17/2014, 8:11:12 PM

Confirmations

6,368,857

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e63d5b212a8b7374c06d9831c0f1dd3506b070f2454ad07add2110724a5a2120

Transactions (1)

Coinbasee63d5b212a8b73…2110724a5a2120

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

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.

5.482 × 10¹⁰⁶(107-digit number)

54825828084095011787…10183573099281969279

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

5.482 × 10¹⁰⁶(107-digit number)

54825828084095011787…10183573099281969279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.096 × 10¹⁰⁷(108-digit number)

10965165616819002357…20367146198563938559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.193 × 10¹⁰⁷(108-digit number)

21930331233638004714…40734292397127877119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.386 × 10¹⁰⁷(108-digit number)

43860662467276009429…81468584794255754239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.772 × 10¹⁰⁷(108-digit number)

87721324934552018859…62937169588511508479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.754 × 10¹⁰⁸(109-digit number)

17544264986910403771…25874339177023016959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.508 × 10¹⁰⁸(109-digit number)

35088529973820807543…51748678354046033919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.017 × 10¹⁰⁸(109-digit number)

70177059947641615087…03497356708092067839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.403 × 10¹⁰⁹(110-digit number)

14035411989528323017…06994713416184135679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.807 × 10¹⁰⁹(110-digit number)

28070823979056646034…13989426832368271359

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 #448,311

Cookie Preferences