Block #86,104

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/27/2013, 9:44:03 PM · Difficulty 9.2906 · 6,705,521 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b87f25febdeba263b1a93534b018d37f2b55dc30cc426d56038300d4c8e6d2f6

View on Chainz ↗

Height

#86,104

Difficulty

9.290585

Transactions

Size

1.09 KB

Version

Bits

094a63c3

Nonce

6,193

Timestamp

7/27/2013, 9:44:03 PM

Confirmations

6,705,521

Merkle Root

473c5a431b2ba2e1dc7933d505f2d64138ae6899d975e08c52e777226ce135e2

Transactions (4)

Coinbase29d016eca31d3c…86fc69ee1c4c25

1 in → 1 out11.6000 XPM109 B

AN38pJA5…BsCnr4tB

725013a03a7c99…b8986e6e6d908d

2 in → 2 out221.9800 XPM375 B

AcVfYzXC…gZNDAAav AWgLSjbC…8aJ5fgEn

9f1241455e98c4…adeb2c8fe31ef0

2 in → 2 out91.6000 XPM375 B

ARoyVBZV…UVwKUoVi AMvWpukB…jT76VW35

66973111cb9e8b…236d1d475bbd64

1 in → 1 out11.6000 XPM158 B

AdPcJirK…3XgpV9WL

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.

9.599 × 10¹¹⁰(111-digit number)

95994291463989768360…47612896903027578279

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

9.599 × 10¹¹⁰(111-digit number)

95994291463989768360…47612896903027578279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.919 × 10¹¹¹(112-digit number)

19198858292797953672…95225793806055156559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.839 × 10¹¹¹(112-digit number)

38397716585595907344…90451587612110313119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.679 × 10¹¹¹(112-digit number)

76795433171191814688…80903175224220626239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.535 × 10¹¹²(113-digit number)

15359086634238362937…61806350448441252479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.071 × 10¹¹²(113-digit number)

30718173268476725875…23612700896882504959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.143 × 10¹¹²(113-digit number)

61436346536953451750…47225401793765009919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.228 × 10¹¹³(114-digit number)

12287269307390690350…94450803587530019839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.457 × 10¹¹³(114-digit number)

24574538614781380700…88901607175060039679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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