Block #71,449

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 6:43:44 PM · Difficulty 8.9932 · 6,742,398 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

db9c430ffb7929c3e39fe4c6d8de24b7c977fcc2a73025203f0f7d2245125b04

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Height

#71,449

Difficulty

8.993201

Transactions

Size

199 B

Version

Bits

08fe426b

Nonce

271

Timestamp

7/20/2013, 6:43:44 PM

Confirmations

6,742,398

Mined by

⛏️ P2SHAHGPtSCNuYeecmqUQuK4cLJv6iGESamBFW

Merkle Root

2e616cf4f2ea0dfc68587975449f5c844ca2879eb7a971d75f1d5bda19b5a922

Transactions (1)

Coinbase2e616cf4f2ea0d…1d5bda19b5a922

1 in → 1 out12.3500 XPM110 B

AHGPtSCN…GESamBFW

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.

2.542 × 10⁹¹(92-digit number)

25429206372717260885…92903215465817399579

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

2.542 × 10⁹¹(92-digit number)

25429206372717260885…92903215465817399579

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.085 × 10⁹¹(92-digit number)

50858412745434521770…85806430931634799159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.017 × 10⁹²(93-digit number)

10171682549086904354…71612861863269598319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.034 × 10⁹²(93-digit number)

20343365098173808708…43225723726539196639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.068 × 10⁹²(93-digit number)

40686730196347617416…86451447453078393279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.137 × 10⁹²(93-digit number)

81373460392695234833…72902894906156786559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.627 × 10⁹³(94-digit number)

16274692078539046966…45805789812313573119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.254 × 10⁹³(94-digit number)

32549384157078093933…91611579624627146239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.509 × 10⁹³(94-digit number)

65098768314156187866…83223159249254292479

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 #71,449

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