Block #143,010

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/31/2013, 8:46:28 AM · Difficulty 9.8373 · 6,648,818 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ef849a90b7999d80ec42a5c57d6dd5b62813669e1fa5b029753a23ec03f34090

View on Chainz ↗

Height

#143,010

Difficulty

9.837319

Transactions

Size

188 B

Version

Bits

09d65a8d

Nonce

77,151

Timestamp

8/31/2013, 8:46:28 AM

Confirmations

6,648,818

Merkle Root

7c9793bc61fd22f4af683a9c541bfaf8023061b60da77ff111f59bf1537a9cb4

Transactions (1)

Coinbase7c9793bc61fd22…f59bf1537a9cb4

1 in → 1 out10.3200 XPM100 B

AbGkvdxH…oihMdBXd

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.

2.208 × 10⁹⁰(91-digit number)

22081535749871309545…29589457604097768299

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

2.208 × 10⁹⁰(91-digit number)

22081535749871309545…29589457604097768299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.416 × 10⁹⁰(91-digit number)

44163071499742619090…59178915208195536599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.832 × 10⁹⁰(91-digit number)

88326142999485238180…18357830416391073199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.766 × 10⁹¹(92-digit number)

17665228599897047636…36715660832782146399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.533 × 10⁹¹(92-digit number)

35330457199794095272…73431321665564292799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.066 × 10⁹¹(92-digit number)

70660914399588190544…46862643331128585599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.413 × 10⁹²(93-digit number)

14132182879917638108…93725286662257171199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.826 × 10⁹²(93-digit number)

28264365759835276217…87450573324514342399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.652 × 10⁹²(93-digit number)

56528731519670552435…74901146649028684799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.130 × 10⁹³(94-digit number)

11305746303934110487…49802293298057369599

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