Block #155,021

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/8/2013, 1:34:17 AM · Difficulty 9.8651 · 6,635,077 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a1654ddb476916a57654edf25a8bcdff5ea3ab82fc53a27bb9e5b9ee74c53cab

View on Chainz ↗

Height

#155,021

Difficulty

9.865095

Transactions

Size

198 B

Version

Bits

09dd76e0

Nonce

430,073

Timestamp

9/8/2013, 1:34:17 AM

Confirmations

6,635,077

Merkle Root

8bffeafa15b479b5bc7eaca13b428944c54fec34ddba4812a2369c8752b83637

Transactions (1)

Coinbase8bffeafa15b479…369c8752b83637

1 in → 1 out10.2600 XPM109 B

AJn9y9Wv…G4raUX4o

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.

1.726 × 10⁹²(93-digit number)

17264512477893401108…97110639900871415999

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

1.726 × 10⁹²(93-digit number)

17264512477893401108…97110639900871415999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.452 × 10⁹²(93-digit number)

34529024955786802216…94221279801742831999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.905 × 10⁹²(93-digit number)

69058049911573604433…88442559603485663999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.381 × 10⁹³(94-digit number)

13811609982314720886…76885119206971327999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.762 × 10⁹³(94-digit number)

27623219964629441773…53770238413942655999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.524 × 10⁹³(94-digit number)

55246439929258883546…07540476827885311999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.104 × 10⁹⁴(95-digit number)

11049287985851776709…15080953655770623999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.209 × 10⁹⁴(95-digit number)

22098575971703553418…30161907311541247999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.419 × 10⁹⁴(95-digit number)

44197151943407106837…60323814623082495999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.839 × 10⁹⁴(95-digit number)

88394303886814213674…20647629246164991999

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