Block #402,949

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/13/2014, 7:21:13 PM · Difficulty 10.4364 · 6,403,114 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

afc1ae1badb9d57c1fd442dee120871b841628d9992162acfe69e2e5e47cdc78

View on Chainz ↗

Height

#402,949

Difficulty

10.436432

Transactions

Size

971 B

Version

Bits

0a6fb9fb

Nonce

35,961

Timestamp

2/13/2014, 7:21:13 PM

Confirmations

6,403,114

Mined by

⛏️ &-kATp4jJhsSxZ4c3nv24ZhThTqRXTbSgR8Qb

Merkle Root

be1a983960439ce8e40ab6f6ead7a19cf09b5bcdc3a25a161ce05fa888841466

Transactions (1)

Coinbasebe1a983960439c…e05fa888841466

1 in → 24 out9.1700 XPM879 B

ATp4jJhs…TbSgR8Qb AUDD9tmA…gJPQLnsz AcgDwGo8…BBFwbjVo AbPcCMg4…719q6mAX AGhdBoQ5…7fGraxgG

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.

1.418 × 10⁹⁹(100-digit number)

14185717091319129720…76694046959815951361

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

1.418 × 10⁹⁹(100-digit number)

14185717091319129720…76694046959815951361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.837 × 10⁹⁹(100-digit number)

28371434182638259441…53388093919631902721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.674 × 10⁹⁹(100-digit number)

56742868365276518883…06776187839263805441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.134 × 10¹⁰⁰(101-digit number)

11348573673055303776…13552375678527610881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.269 × 10¹⁰⁰(101-digit number)

22697147346110607553…27104751357055221761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.539 × 10¹⁰⁰(101-digit number)

45394294692221215106…54209502714110443521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.078 × 10¹⁰⁰(101-digit number)

90788589384442430213…08419005428220887041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.815 × 10¹⁰¹(102-digit number)

18157717876888486042…16838010856441774081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.631 × 10¹⁰¹(102-digit number)

36315435753776972085…33676021712883548161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.263 × 10¹⁰¹(102-digit number)

72630871507553944170…67352043425767096321

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