Block #478,702

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/7/2014, 6:11:10 AM · Difficulty 10.4958 · 6,323,532 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

24fd998ed23550763e8f669fcc10ae15b4386bef63681247b09bbc10e21afcb1

View on Chainz ↗

Height

#478,702

Difficulty

10.495811

Transactions

Size

628 B

Version

Bits

0a7eed74

Nonce

196,289,887

Timestamp

4/7/2014, 6:11:10 AM

Confirmations

6,323,532

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a0da53b9b2ed424888c171e4130c48f04ca9071d27dfdf64c93bb74eccbc6a6d

Transactions (2)

Coinbase470e5e45d08735…ea12f41f642cec

1 in → 1 out9.0700 XPM116 B

AbwWkWZt…kawDhufa

e61d3484204e16…2e8594eff967f9

3 in → 1 out21.3324 XPM420 B

AZrELvLQ…Zn6m5yV6

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.

2.249 × 10⁹⁸(99-digit number)

22493526681103104494…50583720169307165761

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

2.249 × 10⁹⁸(99-digit number)

22493526681103104494…50583720169307165761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.498 × 10⁹⁸(99-digit number)

44987053362206208988…01167440338614331521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.997 × 10⁹⁸(99-digit number)

89974106724412417976…02334880677228663041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.799 × 10⁹⁹(100-digit number)

17994821344882483595…04669761354457326081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.598 × 10⁹⁹(100-digit number)

35989642689764967190…09339522708914652161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.197 × 10⁹⁹(100-digit number)

71979285379529934381…18679045417829304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.439 × 10¹⁰⁰(101-digit number)

14395857075905986876…37358090835658608641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.879 × 10¹⁰⁰(101-digit number)

28791714151811973752…74716181671317217281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.758 × 10¹⁰⁰(101-digit number)

57583428303623947505…49432363342634434561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.151 × 10¹⁰¹(102-digit number)

11516685660724789501…98864726685268869121

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