Block #86,105

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/27/2013, 9:46:28 PM · Difficulty 9.2903 · 6,716,677 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a40d1b509fe65527f02a84e8567ee8d0f8c317ca2674ecdba1606e8d8e24e57f

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Height

#86,105

Difficulty

9.290348

Transactions

Size

209 B

Version

Bits

094a543d

Nonce

243,624

Timestamp

7/27/2013, 9:46:28 PM

Confirmations

6,716,677

Mined by

⛏️ P2SHAU7Hy2ULEBiLut8eWLhMxqzUvnCiDieZSs

Merkle Root

5afa231496e5cb7a16f4534c4d16cf908976b90ec1829a3708f704e0838ebaa5

Transactions (1)

Coinbase5afa231496e5cb…f704e0838ebaa5

1 in → 1 out11.5700 XPM109 B

AU7Hy2UL…CiDieZSs

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.

3.198 × 10¹¹⁸(119-digit number)

31988800595190055579…17218618792645174941

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

3.198 × 10¹¹⁸(119-digit number)

31988800595190055579…17218618792645174941

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.397 × 10¹¹⁸(119-digit number)

63977601190380111159…34437237585290349881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.279 × 10¹¹⁹(120-digit number)

12795520238076022231…68874475170580699761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.559 × 10¹¹⁹(120-digit number)

25591040476152044463…37748950341161399521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.118 × 10¹¹⁹(120-digit number)

51182080952304088927…75497900682322799041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.023 × 10¹²⁰(121-digit number)

10236416190460817785…50995801364645598081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.047 × 10¹²⁰(121-digit number)

20472832380921635571…01991602729291196161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.094 × 10¹²⁰(121-digit number)

40945664761843271142…03983205458582392321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.189 × 10¹²⁰(121-digit number)

81891329523686542284…07966410917164784641

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer