Block #472,062

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/3/2014, 12:48:02 AM · Difficulty 10.4338 · 6,329,739 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b137051f94bc31497d7fb5a2334603928686a07a6e3c8d1adf8b649b56a3c33b

View on Chainz ↗

Height

#472,062

Difficulty

10.433765

Transactions

Size

834 B

Version

Bits

0a6f0b34

Nonce

8,174

Timestamp

4/3/2014, 12:48:02 AM

Confirmations

6,329,739

Mined by

⛏️ 3aS<ATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

7fc4af38354da70e93d455425b354f2ca45f1b815a11918ae45c792f111ec6ba

Transactions (1)

Coinbase7fc4af38354da7…5c792f111ec6ba

1 in → 20 out9.1700 XPM743 B

ATKK7iFz…wZm46KN1 AdwTEXyC…NwbVbqZV AamykSCW…5Mjzpr7i AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR

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.

1.460 × 10⁹⁶(97-digit number)

14609376379823297630…82303244260876651521

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

1.460 × 10⁹⁶(97-digit number)

14609376379823297630…82303244260876651521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.921 × 10⁹⁶(97-digit number)

29218752759646595261…64606488521753303041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.843 × 10⁹⁶(97-digit number)

58437505519293190523…29212977043506606081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.168 × 10⁹⁷(98-digit number)

11687501103858638104…58425954087013212161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.337 × 10⁹⁷(98-digit number)

23375002207717276209…16851908174026424321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.675 × 10⁹⁷(98-digit number)

46750004415434552418…33703816348052848641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.350 × 10⁹⁷(98-digit number)

93500008830869104836…67407632696105697281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.870 × 10⁹⁸(99-digit number)

18700001766173820967…34815265392211394561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.740 × 10⁹⁸(99-digit number)

37400003532347641934…69630530784422789121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.480 × 10⁹⁸(99-digit number)

74800007064695283869…39261061568845578241

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