Block #315,131

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/16/2013, 8:44:49 AM · Difficulty 10.0859 · 6,523,194 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

17ba99ba9b6ea065a12c9b5fc8ea2b8a80ef3e50cc029e20f3ce05862f13972b

View on Chainz ↗

Height

#315,131

Difficulty

10.085918

Transactions

Size

208 B

Version

Bits

0a15fec1

Nonce

21,233

Timestamp

12/16/2013, 8:44:49 AM

Confirmations

6,523,194

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f1777bf486409bb354be16d1653435ba5ccad1418f283cb80d54a147e62cd6d2

Transactions (1)

Coinbasef1777bf486409b…54a147e62cd6d2

1 in → 1 out9.8200 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.

1.438 × 10⁹⁹(100-digit number)

14381315320655107595…70956744692554239999

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

1.438 × 10⁹⁹(100-digit number)

14381315320655107595…70956744692554239999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.876 × 10⁹⁹(100-digit number)

28762630641310215190…41913489385108479999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.752 × 10⁹⁹(100-digit number)

57525261282620430380…83826978770216959999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.150 × 10¹⁰⁰(101-digit number)

11505052256524086076…67653957540433919999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.301 × 10¹⁰⁰(101-digit number)

23010104513048172152…35307915080867839999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.602 × 10¹⁰⁰(101-digit number)

46020209026096344304…70615830161735679999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.204 × 10¹⁰⁰(101-digit number)

92040418052192688608…41231660323471359999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.840 × 10¹⁰¹(102-digit number)

18408083610438537721…82463320646942719999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.681 × 10¹⁰¹(102-digit number)

36816167220877075443…64926641293885439999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.363 × 10¹⁰¹(102-digit number)

73632334441754150887…29853282587770879999

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #315,131

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