Block #495,071

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 11:24:49 AM · Difficulty 10.7302 · 6,297,610 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9cdad79d9bf8c28db607bdc3416cded483e5e4dd791cc3d610297f1c24136424

View on Chainz ↗

Height

#495,071

Difficulty

10.730240

Transactions

Size

867 B

Version

Bits

0abaf108

Nonce

70,642

Timestamp

4/16/2014, 11:24:49 AM

Confirmations

6,297,610

Merkle Root

1c9ddb03808ac18da3e806bfdcc72d75677c1ed1710bffb05050052f64b74c78

Transactions (1)

Coinbase1c9ddb03808ac1…50052f64b74c78

1 in → 21 out8.6700 XPM777 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3

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.

6.762 × 10⁹⁵(96-digit number)

67622955407540691897…47375140154657167679

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

6.762 × 10⁹⁵(96-digit number)

67622955407540691897…47375140154657167679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.352 × 10⁹⁶(97-digit number)

13524591081508138379…94750280309314335359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.704 × 10⁹⁶(97-digit number)

27049182163016276759…89500560618628670719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.409 × 10⁹⁶(97-digit number)

54098364326032553518…79001121237257341439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.081 × 10⁹⁷(98-digit number)

10819672865206510703…58002242474514682879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.163 × 10⁹⁷(98-digit number)

21639345730413021407…16004484949029365759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.327 × 10⁹⁷(98-digit number)

43278691460826042814…32008969898058731519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.655 × 10⁹⁷(98-digit number)

86557382921652085629…64017939796117463039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.731 × 10⁹⁸(99-digit number)

17311476584330417125…28035879592234926079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.462 × 10⁹⁸(99-digit number)

34622953168660834251…56071759184469852159

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