Block #506,873

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/23/2014, 8:52:35 AM · Difficulty 10.8153 · 6,287,778 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8edd1622c5f57c1d1a363c0eef829979754c9472db411af37c28924630983989

View on Chainz ↗

Height

#506,873

Difficulty

10.815255

Transactions

Size

800 B

Version

Bits

0ad0b48d

Nonce

83,640

Timestamp

4/23/2014, 8:52:35 AM

Confirmations

6,287,778

Mined by

⛏️ aSWAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

bba702e6c846eb65811ad784da4495086a265e47ec9d362427383de89f164a3d

Transactions (1)

Coinbasebba702e6c846eb…383de89f164a3d

1 in → 19 out8.5400 XPM709 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

9.532 × 10⁹⁵(96-digit number)

95329372723522195564…73074143778856744449

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

9.532 × 10⁹⁵(96-digit number)

95329372723522195564…73074143778856744449

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.906 × 10⁹⁶(97-digit number)

19065874544704439112…46148287557713488899

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.813 × 10⁹⁶(97-digit number)

38131749089408878225…92296575115426977799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.626 × 10⁹⁶(97-digit number)

76263498178817756451…84593150230853955599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.525 × 10⁹⁷(98-digit number)

15252699635763551290…69186300461707911199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.050 × 10⁹⁷(98-digit number)

30505399271527102580…38372600923415822399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.101 × 10⁹⁷(98-digit number)

61010798543054205161…76745201846831644799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.220 × 10⁹⁸(99-digit number)

12202159708610841032…53490403693663289599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.440 × 10⁹⁸(99-digit number)

24404319417221682064…06980807387326579199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.880 × 10⁹⁸(99-digit number)

48808638834443364129…13961614774653158399

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