Block #402,546

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/13/2014, 12:34:40 PM · Difficulty 10.4368 · 6,403,904 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ebe5fbaa74dbc749636c99e180a884bcd985c40acc79e0aab6e97fbd59a572ab

View on Chainz ↗

Height

#402,546

Difficulty

10.436782

Transactions

Size

209 B

Version

Bits

0a6fd0f1

Nonce

783,494

Timestamp

2/13/2014, 12:34:40 PM

Confirmations

6,403,904

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8663d0cd44ce1a858c750308f5241104fcbce101a08d881fba4cc2844678a699

Transactions (1)

Coinbase8663d0cd44ce1a…4cc2844678a699

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

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.

1.068 × 10¹⁰¹(102-digit number)

10689921465684951901…05209438110897006601

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

1.068 × 10¹⁰¹(102-digit number)

10689921465684951901…05209438110897006601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.137 × 10¹⁰¹(102-digit number)

21379842931369903802…10418876221794013201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.275 × 10¹⁰¹(102-digit number)

42759685862739807605…20837752443588026401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.551 × 10¹⁰¹(102-digit number)

85519371725479615211…41675504887176052801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.710 × 10¹⁰²(103-digit number)

17103874345095923042…83351009774352105601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.420 × 10¹⁰²(103-digit number)

34207748690191846084…66702019548704211201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.841 × 10¹⁰²(103-digit number)

68415497380383692169…33404039097408422401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.368 × 10¹⁰³(104-digit number)

13683099476076738433…66808078194816844801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.736 × 10¹⁰³(104-digit number)

27366198952153476867…33616156389633689601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.473 × 10¹⁰³(104-digit number)

54732397904306953735…67232312779267379201

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 #402,546

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