Block #1,331,722

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/18/2015, 6:49:47 AM · Difficulty 10.8408 · 5,475,899 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

05179f8c7f27900b9a7a1570b2cc46d5b443beaf4f6473f031e487d7cdc303a4

View on Chainz ↗

Height

#1,331,722

Difficulty

10.840773

Transactions

Size

201 B

Version

Bits

0ad73cea

Nonce

398,976

Timestamp

11/18/2015, 6:49:47 AM

Confirmations

5,475,899

Mined by

⛏️ P2SHALyrjdQznLJKBtm9rLYDEPdqpPUZoc3FAD

Merkle Root

c81d26eb5258582234ab616ca270897f561320d771bb2c899c3969f5f62c7a26

Transactions (1)

Coinbasec81d26eb525858…3969f5f62c7a26

1 in → 1 out8.5000 XPM109 B

ALyrjdQz…UZoc3FAD

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.

3.461 × 10⁹⁹(100-digit number)

34617317132332918926…13609015054220194701

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

3.461 × 10⁹⁹(100-digit number)

34617317132332918926…13609015054220194701

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.923 × 10⁹⁹(100-digit number)

69234634264665837853…27218030108440389401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.384 × 10¹⁰⁰(101-digit number)

13846926852933167570…54436060216880778801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.769 × 10¹⁰⁰(101-digit number)

27693853705866335141…08872120433761557601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.538 × 10¹⁰⁰(101-digit number)

55387707411732670282…17744240867523115201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.107 × 10¹⁰¹(102-digit number)

11077541482346534056…35488481735046230401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.215 × 10¹⁰¹(102-digit number)

22155082964693068113…70976963470092460801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.431 × 10¹⁰¹(102-digit number)

44310165929386136226…41953926940184921601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.862 × 10¹⁰¹(102-digit number)

88620331858772272452…83907853880369843201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.772 × 10¹⁰²(103-digit number)

17724066371754454490…67815707760739686401

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

Block #1,331,722

Cookie Preferences