Block #1,119,886

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/20/2015, 9:45:01 PM · Difficulty 10.9337 · 5,683,891 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3fba6580f8a546233e9839a638a8d53baba45290c063f071bb93cff62517b5aa

View on Chainz ↗

Height

#1,119,886

Difficulty

10.933658

Transactions

Size

243 B

Version

Bits

0aef0431

Nonce

273,404,843

Timestamp

6/20/2015, 9:45:01 PM

Confirmations

5,683,891

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

abcdd5ed6cd1c615a3c61b9573716238dbd96d05493075c54cdb24c3ac375726

Transactions (1)

Coinbaseabcdd5ed6cd1c6…db24c3ac375726

1 in → 2 out8.3500 XPM152 B

APGBorYS…QnZrTNSi ALPu3s2c…EJXLjVFh

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.

3.114 × 10⁹⁶(97-digit number)

31145164665919488367…42937592551319675201

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

3.114 × 10⁹⁶(97-digit number)

31145164665919488367…42937592551319675201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.229 × 10⁹⁶(97-digit number)

62290329331838976734…85875185102639350401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.245 × 10⁹⁷(98-digit number)

12458065866367795346…71750370205278700801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.491 × 10⁹⁷(98-digit number)

24916131732735590693…43500740410557401601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.983 × 10⁹⁷(98-digit number)

49832263465471181387…87001480821114803201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.966 × 10⁹⁷(98-digit number)

99664526930942362775…74002961642229606401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.993 × 10⁹⁸(99-digit number)

19932905386188472555…48005923284459212801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.986 × 10⁹⁸(99-digit number)

39865810772376945110…96011846568918425601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.973 × 10⁹⁸(99-digit number)

79731621544753890220…92023693137836851201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.594 × 10⁹⁹(100-digit number)

15946324308950778044…84047386275673702401

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer