Block #77,446

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2013, 10:18:28 AM · Difficulty 9.1725 · 6,717,354 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8c780d168e458e9e8044f29d695f605a0cfb5d922c3a76768a5e2de256eca4bf

View on Chainz ↗

Height

#77,446

Difficulty

9.172495

Transactions

Size

16.62 KB

Version

Bits

092c28a7

Nonce

1,263

Timestamp

7/22/2013, 10:18:28 AM

Confirmations

6,717,354

Mined by

⛏️ P2SHAZKYkcRPtge3X6pdsw6dAWTung6gyjU3Pn

Merkle Root

cde8f0179657320265f31b8bb3efc0317c8dd7a88747d2cd261f3f24ce911d1c

Transactions (3)

Coinbase5567078b59d884…cdbef58cfa5316

1 in → 1 out12.0500 XPM110 B

AZKYkcRP…6gyjU3Pn

8589d1143208d0…59f948e37cd1ab

73 in → 2 out903.7400 XPM8.21 KB

ANBGBvzR…CgPGtqfX ASRYh8GP…WiYakb8i

776a26dcfdbc90…8036c38e8e7212

73 in → 2 out903.3000 XPM8.21 KB

AduwKP5J…wp1LyLxL ARTVb17q…rifMjGeB

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.

1.279 × 10⁹⁸(99-digit number)

12797299934494534595…36031497058545210729

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

1.279 × 10⁹⁸(99-digit number)

12797299934494534595…36031497058545210729

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.559 × 10⁹⁸(99-digit number)

25594599868989069191…72062994117090421459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.118 × 10⁹⁸(99-digit number)

51189199737978138382…44125988234180842919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.023 × 10⁹⁹(100-digit number)

10237839947595627676…88251976468361685839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.047 × 10⁹⁹(100-digit number)

20475679895191255352…76503952936723371679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.095 × 10⁹⁹(100-digit number)

40951359790382510705…53007905873446743359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.190 × 10⁹⁹(100-digit number)

81902719580765021411…06015811746893486719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.638 × 10¹⁰⁰(101-digit number)

16380543916153004282…12031623493786973439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.276 × 10¹⁰⁰(101-digit number)

32761087832306008564…24063246987573946879

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer