Block #62,984

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 10:38:40 PM · Difficulty 8.9779 · 6,742,376 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

78844509eaab91e5bda2c39eb3c0e0e8072c4eb0f48c3426be583c5013567c0f

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Height

#62,984

Difficulty

8.977950

Transactions

Size

579 B

Version

Bits

08fa5ae7

Nonce

Timestamp

7/18/2013, 10:38:40 PM

Confirmations

6,742,376

Mined by

⛏️ P2SHAQC8uaMYw4bnAtaepjaTJ4skeWJQg5Vnxm

Merkle Root

7df2b0547596de0880bbb456837cb6d2195d5eeddb3b934bc3dccfdda369d7e8

Transactions (2)

Coinbase4d1204d71191c1…671f4884e5304d

1 in → 1 out12.4000 XPM110 B

AQC8uaMY…JQg5Vnxm

74c422ee75d958…787c5deeb60931

2 in → 2 out115.5140 XPM376 B

ANLUKCVZ…x71w4m7f AdM8MrtT…pKqZyGtr

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.

1.456 × 10¹⁰¹(102-digit number)

14563085474211715010…62268819071407253461

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

1.456 × 10¹⁰¹(102-digit number)

14563085474211715010…62268819071407253461

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.912 × 10¹⁰¹(102-digit number)

29126170948423430021…24537638142814506921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.825 × 10¹⁰¹(102-digit number)

58252341896846860042…49075276285629013841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.165 × 10¹⁰²(103-digit number)

11650468379369372008…98150552571258027681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.330 × 10¹⁰²(103-digit number)

23300936758738744017…96301105142516055361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.660 × 10¹⁰²(103-digit number)

46601873517477488034…92602210285032110721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.320 × 10¹⁰²(103-digit number)

93203747034954976068…85204420570064221441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.864 × 10¹⁰³(104-digit number)

18640749406990995213…70408841140128442881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.728 × 10¹⁰³(104-digit number)

37281498813981990427…40817682280256885761

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