Block #90,566

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/31/2013, 5:58:44 AM · Difficulty 9.2391 · 6,713,457 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

273c9f2a0123587603057924602fe5bec1bddd23930d2f19824305848b580590

View on Chainz ↗

Height

#90,566

Difficulty

9.239114

Transactions

Size

208 B

Version

Bits

093d3694

Nonce

31,713

Timestamp

7/31/2013, 5:58:44 AM

Confirmations

6,713,457

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

ff1000cdb16559c13a144ef53694dc267add2a691a636fa4df41f6b330dc0670

Transactions (1)

Coinbaseff1000cdb16559…41f6b330dc0670

1 in → 1 out11.7000 XPM109 B

AH8MuWec…2bVG62mK

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.

1.921 × 10¹¹⁵(116-digit number)

19218185118204564713…32014475964806288241

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

1.921 × 10¹¹⁵(116-digit number)

19218185118204564713…32014475964806288241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.843 × 10¹¹⁵(116-digit number)

38436370236409129426…64028951929612576481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.687 × 10¹¹⁵(116-digit number)

76872740472818258852…28057903859225152961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.537 × 10¹¹⁶(117-digit number)

15374548094563651770…56115807718450305921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.074 × 10¹¹⁶(117-digit number)

30749096189127303540…12231615436900611841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.149 × 10¹¹⁶(117-digit number)

61498192378254607081…24463230873801223681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.229 × 10¹¹⁷(118-digit number)

12299638475650921416…48926461747602447361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.459 × 10¹¹⁷(118-digit number)

24599276951301842832…97852923495204894721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.919 × 10¹¹⁷(118-digit number)

49198553902603685665…95705846990409789441

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