Block #314,888

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/16/2013, 5:22:41 AM · Difficulty 10.0784 · 6,481,938 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5a4026e1fd76f79da416cdac002f0398e939a05aef9417ad2f3507e72332d2ed

View on Chainz ↗

Height

#314,888

Difficulty

10.078368

Transactions

Size

1.08 KB

Version

Bits

0a140fee

Nonce

68,738

Timestamp

12/16/2013, 5:22:41 AM

Confirmations

6,481,938

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

00de9a1959412f0212e1d5182500ea39436d5df7cca6caa53602021b7d0c3d9e

Transactions (1)

Coinbase00de9a1959412f…02021b7d0c3d9e

1 in → 28 out9.8100 XPM1015 B

Aac9Hjdg…P4ktypc3 AZ2pPuKg…95SN2Yr7 ASWX42VM…XypQABkY AJzWx2VD…j4ZSMit5 APCGUbeg…DwpndUSB

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.

8.622 × 10⁹⁹(100-digit number)

86228032111237915120…66398530244182772639

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

8.622 × 10⁹⁹(100-digit number)

86228032111237915120…66398530244182772639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.724 × 10¹⁰⁰(101-digit number)

17245606422247583024…32797060488365545279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.449 × 10¹⁰⁰(101-digit number)

34491212844495166048…65594120976731090559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.898 × 10¹⁰⁰(101-digit number)

68982425688990332096…31188241953462181119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.379 × 10¹⁰¹(102-digit number)

13796485137798066419…62376483906924362239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.759 × 10¹⁰¹(102-digit number)

27592970275596132838…24752967813848724479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.518 × 10¹⁰¹(102-digit number)

55185940551192265677…49505935627697448959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.103 × 10¹⁰²(103-digit number)

11037188110238453135…99011871255394897919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.207 × 10¹⁰²(103-digit number)

22074376220476906270…98023742510789795839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.414 × 10¹⁰²(103-digit number)

44148752440953812541…96047485021579591679

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