Block #145,415

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/1/2013, 9:21:09 PM · Difficulty 9.8441 · 6,658,310 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a4aea9df4158718a1f5714db6a4ca0b0b63eddde5c4e1ddace4c2c5971e1323e

View on Chainz ↗

Height

#145,415

Difficulty

9.844067

Transactions

Size

986 B

Version

Bits

09d814cb

Nonce

124,008

Timestamp

9/1/2013, 9:21:09 PM

Confirmations

6,658,310

Mined by

⛏️ P2SHAHmvhRqWL5g4Fhy2RMfdSpypuGqgG5FwBR

Merkle Root

dbba13033a7bb846c3bfad06b3750376a6d57c98f5a9441be5d8c8707722b186

Transactions (2)

Coinbaseca93544bd6e0ef…e7dc928903091b

1 in → 1 out10.3100 XPM109 B

AHmvhRqW…qgG5FwBR

400127239d71ab…14312f6d1192a3

5 in → 1 out227.9700 XPM787 B

AaZTHvEh…QXHS2iBB

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.

4.463 × 10⁹³(94-digit number)

44635963152696171458…89118369243748729601

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

4.463 × 10⁹³(94-digit number)

44635963152696171458…89118369243748729601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.927 × 10⁹³(94-digit number)

89271926305392342916…78236738487497459201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.785 × 10⁹⁴(95-digit number)

17854385261078468583…56473476974994918401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.570 × 10⁹⁴(95-digit number)

35708770522156937166…12946953949989836801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.141 × 10⁹⁴(95-digit number)

71417541044313874332…25893907899979673601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.428 × 10⁹⁵(96-digit number)

14283508208862774866…51787815799959347201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.856 × 10⁹⁵(96-digit number)

28567016417725549733…03575631599918694401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.713 × 10⁹⁵(96-digit number)

57134032835451099466…07151263199837388801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.142 × 10⁹⁶(97-digit number)

11426806567090219893…14302526399674777601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.285 × 10⁹⁶(97-digit number)

22853613134180439786…28605052799349555201

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