Block #179,118

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/24/2013, 8:52:06 PM · Difficulty 9.8636 · 6,633,884 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fdcb43dd17075a30b52bfacd40053288c464e510d46dfc4cfba7ff6f4676905c

View on Chainz ↗

Height

#179,118

Difficulty

9.863581

Transactions

Size

1.59 KB

Version

Bits

09dd13a3

Nonce

362,195

Timestamp

9/24/2013, 8:52:06 PM

Confirmations

6,633,884

Mined by

⛏️ P2SHALmzH2QvJKtTiH7BbS7wXXXMop2AtM8SeA

Merkle Root

e8b2d29f62aeeb7bd3ea6818b7a6869af001b7da9b66563ae0b7f9481516e293

Transactions (2)

Coinbase1abe4c90ac8085…fc395ed1c7c01c

1 in → 1 out10.2890 XPM109 B

ALmzH2Qv…2AtM8SeA

b8f538b7f7d5a6…eacb1b663727fc

11 in → 1 out78.0000 XPM1.40 KB

AcL33TiX…ZwPeWWWg

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.

5.380 × 10⁹¹(92-digit number)

53804994669600032599…38046308581119861119

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

5.380 × 10⁹¹(92-digit number)

53804994669600032599…38046308581119861119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.076 × 10⁹²(93-digit number)

10760998933920006519…76092617162239722239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.152 × 10⁹²(93-digit number)

21521997867840013039…52185234324479444479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.304 × 10⁹²(93-digit number)

43043995735680026079…04370468648958888959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.608 × 10⁹²(93-digit number)

86087991471360052158…08740937297917777919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.721 × 10⁹³(94-digit number)

17217598294272010431…17481874595835555839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.443 × 10⁹³(94-digit number)

34435196588544020863…34963749191671111679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.887 × 10⁹³(94-digit number)

68870393177088041727…69927498383342223359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.377 × 10⁹⁴(95-digit number)

13774078635417608345…39854996766684446719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #179,118

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