Block #495,442

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 3:23:02 PM · Difficulty 10.7373 · 6,296,131 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7ee1cf23ab2fbfd4a5c5f6f08d8ca7b4471e55e5224a87b254a206f311ca168e

View on Chainz ↗

Height

#495,442

Difficulty

10.737338

Transactions

Size

799 B

Version

Bits

0abcc236

Nonce

5,186

Timestamp

4/16/2014, 3:23:02 PM

Confirmations

6,296,131

Merkle Root

72509140251a05e0dfd74f11e702bbecd719db54c5b286b74a6ba2fc8d6e0a98

Transactions (1)

Coinbase72509140251a05…6ba2fc8d6e0a98

1 in → 19 out8.6517 XPM709 B

AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ AJtNW28X…Syb4Ph5j AUbecsVa…i8zo8qRf

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.

4.223 × 10⁹³(94-digit number)

42239882078420131708…37043184807890216959

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

4.223 × 10⁹³(94-digit number)

42239882078420131708…37043184807890216959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.447 × 10⁹³(94-digit number)

84479764156840263416…74086369615780433919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.689 × 10⁹⁴(95-digit number)

16895952831368052683…48172739231560867839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.379 × 10⁹⁴(95-digit number)

33791905662736105366…96345478463121735679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.758 × 10⁹⁴(95-digit number)

67583811325472210732…92690956926243471359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.351 × 10⁹⁵(96-digit number)

13516762265094442146…85381913852486942719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.703 × 10⁹⁵(96-digit number)

27033524530188884293…70763827704973885439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.406 × 10⁹⁵(96-digit number)

54067049060377768586…41527655409947770879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.081 × 10⁹⁶(97-digit number)

10813409812075553717…83055310819895541759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.162 × 10⁹⁶(97-digit number)

21626819624151107434…66110621639791083519

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