Block #39,074

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/14/2013, 12:56:31 PM · Difficulty 8.2728 · 6,787,037 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3ed67199cb556e84a7cde56557e6cad133fc8fa7460527eefe9513b986635289

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Height

#39,074

Difficulty

8.272761

Transactions

Size

206 B

Version

Bits

0845d3aa

Nonce

Timestamp

7/14/2013, 12:56:31 PM

Confirmations

6,787,037

Mined by

⛏️ P2SHAMAsrnszMdk7D2xh8TKDhzb5Ai99mSq6AM

Merkle Root

1ccf3e4e1568f3c9149a9ec8f21607a780f3b5afe6b9f312075fd209458b7748

Transactions (1)

Coinbase1ccf3e4e1568f3…5fd209458b7748

1 in → 1 out14.5900 XPM109 B

AMAsrnsz…99mSq6AM

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.

3.275 × 10¹¹⁰(111-digit number)

32750295455848584558…53019757449798682601

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

3.275 × 10¹¹⁰(111-digit number)

32750295455848584558…53019757449798682601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.550 × 10¹¹⁰(111-digit number)

65500590911697169116…06039514899597365201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.310 × 10¹¹¹(112-digit number)

13100118182339433823…12079029799194730401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.620 × 10¹¹¹(112-digit number)

26200236364678867646…24158059598389460801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.240 × 10¹¹¹(112-digit number)

52400472729357735293…48316119196778921601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.048 × 10¹¹²(113-digit number)

10480094545871547058…96632238393557843201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.096 × 10¹¹²(113-digit number)

20960189091743094117…93264476787115686401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.192 × 10¹¹²(113-digit number)

41920378183486188234…86528953574231372801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.384 × 10¹¹²(113-digit number)

83840756366972376469…73057907148462745601

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #39,074

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