Block #48,753

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 4:53:05 PM · Difficulty 8.8515 · 6,754,619 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c25f5808185a0a24eeef1bbcf1d909ca91470aa5b9c709a5755dcfd29bf60825

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Height

#48,753

Difficulty

8.851514

Transactions

Size

1.58 KB

Version

Bits

08d9fcce

Nonce

695

Timestamp

7/15/2013, 4:53:05 PM

Confirmations

6,754,619

Mined by

⛏️ P2SHAVBvhe9e3frDGdzGkWALwJaNKrYbxQd77o

Merkle Root

d191d74358abe6f4ab994d481aea4fabc3ea56ad02bc586ae51436d78720f9df

Transactions (2)

Coinbase723785d6995850…6c8c22d8dbc191

1 in → 1 out12.7700 XPM110 B

AVBvhe9e…YbxQd77o

c12cb5efd549f8…b97874f02c9cc9

9 in → 2 out9526.2260 XPM1.38 KB

AQPRwnDq…2TkKuiEn AQ7f6oU5…PNUomcKU

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.

4.324 × 10¹⁰³(104-digit number)

43247816703278638235…49516462225216680641

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

4.324 × 10¹⁰³(104-digit number)

43247816703278638235…49516462225216680641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.649 × 10¹⁰³(104-digit number)

86495633406557276471…99032924450433361281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.729 × 10¹⁰⁴(105-digit number)

17299126681311455294…98065848900866722561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.459 × 10¹⁰⁴(105-digit number)

34598253362622910588…96131697801733445121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.919 × 10¹⁰⁴(105-digit number)

69196506725245821177…92263395603466890241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.383 × 10¹⁰⁵(106-digit number)

13839301345049164235…84526791206933780481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.767 × 10¹⁰⁵(106-digit number)

27678602690098328470…69053582413867560961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.535 × 10¹⁰⁵(106-digit number)

55357205380196656941…38107164827735121921

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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