Block #77,262

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2013, 8:43:15 AM · Difficulty 9.1573 · 6,714,156 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f8b87878622d95400876532dbe785d54ffb6e6c4cd09c91d2248c4b34178fc56

View on Chainz ↗

Height

#77,262

Difficulty

9.157287

Transactions

Size

201 B

Version

Bits

092843ee

Nonce

1,051

Timestamp

7/22/2013, 8:43:15 AM

Confirmations

6,714,156

Merkle Root

784e08403eefda4142b2e8ca56203150cf96a54af7fb15dada6d08462c4e43af

Transactions (1)

Coinbase784e08403eefda…6d08462c4e43af

1 in → 1 out11.9100 XPM110 B

AZHRWoCj…YmyiuBx4

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.

1.364 × 10⁹⁸(99-digit number)

13644319010118938890…06201706707832788189

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

1.364 × 10⁹⁸(99-digit number)

13644319010118938890…06201706707832788189

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.728 × 10⁹⁸(99-digit number)

27288638020237877780…12403413415665576379

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.457 × 10⁹⁸(99-digit number)

54577276040475755560…24806826831331152759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.091 × 10⁹⁹(100-digit number)

10915455208095151112…49613653662662305519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.183 × 10⁹⁹(100-digit number)

21830910416190302224…99227307325324611039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.366 × 10⁹⁹(100-digit number)

43661820832380604448…98454614650649222079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.732 × 10⁹⁹(100-digit number)

87323641664761208897…96909229301298444159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.746 × 10¹⁰⁰(101-digit number)

17464728332952241779…93818458602596888319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.492 × 10¹⁰⁰(101-digit number)

34929456665904483558…87636917205193776639

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