Block #363,135

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/17/2014, 5:05:46 AM · Difficulty 10.4141 · 6,436,398 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d95bd8bfda2657a02a9a867ffe4f9a522bf01b6cbde1ebe48520cb8430ec0bdc

View on Chainz ↗

Height

#363,135

Difficulty

10.414098

Transactions

Size

847 B

Version

Bits

0a6a024c

Nonce

1,474

Timestamp

1/17/2014, 5:05:46 AM

Confirmations

6,436,398

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

875675db8288dfbe8b8aa22669a959eff4bd825cef661e05099e51c627e031df

Transactions (2)

Coinbase7ad2ead70231cf…92e99365e913da

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

4d315852527807…b2426d9673500c

4 in → 1 out12.0690 XPM638 B

APVe9Ndp…QXjhNzJ8

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.

1.107 × 10¹⁰²(103-digit number)

11071086434285496337…98322388707188408321

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

1.107 × 10¹⁰²(103-digit number)

11071086434285496337…98322388707188408321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.214 × 10¹⁰²(103-digit number)

22142172868570992674…96644777414376816641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.428 × 10¹⁰²(103-digit number)

44284345737141985349…93289554828753633281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.856 × 10¹⁰²(103-digit number)

88568691474283970699…86579109657507266561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.771 × 10¹⁰³(104-digit number)

17713738294856794139…73158219315014533121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.542 × 10¹⁰³(104-digit number)

35427476589713588279…46316438630029066241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.085 × 10¹⁰³(104-digit number)

70854953179427176559…92632877260058132481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.417 × 10¹⁰⁴(105-digit number)

14170990635885435311…85265754520116264961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.834 × 10¹⁰⁴(105-digit number)

28341981271770870623…70531509040232529921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.668 × 10¹⁰⁴(105-digit number)

56683962543541741247…41063018080465059841

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