Block #78,883

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/23/2013, 4:11:03 AM · Difficulty 9.2300 · 6,729,246 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1e7556f5f63f5ebef3c4bda07ed78b50489ea503c9aa4f5c64c7d8501c9373ca

View on Chainz ↗

Height

#78,883

Difficulty

9.229990

Transactions

Size

210 B

Version

Bits

093ae0a5

Nonce

230

Timestamp

7/23/2013, 4:11:03 AM

Confirmations

6,729,246

Mined by

⛏️ P2SHAPDVqt34NEoKmRGPqZSk2zcL1GXWrhV4UM

Merkle Root

aca8f39aa2c6bea939d138d6893a8d7b30bd0c02cee9a4d271b6185fa3025b13

Transactions (1)

Coinbaseaca8f39aa2c6be…b6185fa3025b13

1 in → 1 out11.7200 XPM110 B

APDVqt34…XWrhV4UM

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.

9.847 × 10¹¹⁸(119-digit number)

98478335866360889307…03086232358860860539

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

9.847 × 10¹¹⁸(119-digit number)

98478335866360889307…03086232358860860539

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.969 × 10¹¹⁹(120-digit number)

19695667173272177861…06172464717721721079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.939 × 10¹¹⁹(120-digit number)

39391334346544355722…12344929435443442159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.878 × 10¹¹⁹(120-digit number)

78782668693088711445…24689858870886884319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.575 × 10¹²⁰(121-digit number)

15756533738617742289…49379717741773768639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.151 × 10¹²⁰(121-digit number)

31513067477235484578…98759435483547537279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.302 × 10¹²⁰(121-digit number)

63026134954470969156…97518870967095074559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.260 × 10¹²¹(122-digit number)

12605226990894193831…95037741934190149119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.521 × 10¹²¹(122-digit number)

25210453981788387662…90075483868380298239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.042 × 10¹²¹(122-digit number)

50420907963576775325…80150967736760596479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #78,883

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