Block #79,247

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 8:47:11 AM · Difficulty 9.2433 · 6,730,635 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

51693c9b7a1a20a2d0c2b8990c07ed579e3c8fe3347077cce53969402d7e3ecd

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Height

#79,247

Difficulty

9.243348

Transactions

Size

2.57 KB

Version

Bits

093e4c08

Nonce

1,160

Timestamp

7/23/2013, 8:47:11 AM

Confirmations

6,730,635

Mined by

⛏️ P2SHAUXiuBtwW9xJwoR1H5VwFHZZFYbzdHu66Y

Merkle Root

31f08c32e6e019e6d3c052ebb796aaf04501a27427f6911ed7c187ac24106e53

Transactions (2)

Coinbase2ca7c495312556…b1d01f15aaddf0

1 in → 1 out11.7200 XPM110 B

AUXiuBtw…bzdHu66Y

63b16cbbe60ce7…a4a57ff22413fa

20 in → 2 out219.8300 XPM2.37 KB

Ab8afhHa…cNwnVLP1 Ab4rdENu…TQCgYmjg

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.

6.113 × 10¹⁰⁵(106-digit number)

61137027868770724933…70850671032255903151

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

6.113 × 10¹⁰⁵(106-digit number)

61137027868770724933…70850671032255903151

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.222 × 10¹⁰⁶(107-digit number)

12227405573754144986…41701342064511806301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.445 × 10¹⁰⁶(107-digit number)

24454811147508289973…83402684129023612601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.890 × 10¹⁰⁶(107-digit number)

48909622295016579946…66805368258047225201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.781 × 10¹⁰⁶(107-digit number)

97819244590033159893…33610736516094450401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.956 × 10¹⁰⁷(108-digit number)

19563848918006631978…67221473032188900801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.912 × 10¹⁰⁷(108-digit number)

39127697836013263957…34442946064377801601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.825 × 10¹⁰⁷(108-digit number)

78255395672026527914…68885892128755603201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.565 × 10¹⁰⁸(109-digit number)

15651079134405305582…37771784257511206401

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 #79,247

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