Block #83,550

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/26/2013, 5:52:50 AM · Difficulty 9.2669 · 6,719,148 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5a0558a5e35e5e5b38d2a2cdd333120ac9b9e2a0f8ee21c6e3f60ff43ce92321

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Height

#83,550

Difficulty

9.266911

Transactions

Size

212 B

Version

Bits

09445442

Nonce

43,579

Timestamp

7/26/2013, 5:52:50 AM

Confirmations

6,719,148

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

cfa4a6ce5e4f26b229aa35e67d9bcb38789e59af03583f1b1991ae8aac676cdb

Transactions (1)

Coinbasecfa4a6ce5e4f26…91ae8aac676cdb

1 in → 1 out11.6300 XPM109 B

ATe7tG7X…yczDSDEp

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.

1.778 × 10¹²⁶(127-digit number)

17785135879565807168…30376277216672094221

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

1.778 × 10¹²⁶(127-digit number)

17785135879565807168…30376277216672094221

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.557 × 10¹²⁶(127-digit number)

35570271759131614337…60752554433344188441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.114 × 10¹²⁶(127-digit number)

71140543518263228674…21505108866688376881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.422 × 10¹²⁷(128-digit number)

14228108703652645734…43010217733376753761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.845 × 10¹²⁷(128-digit number)

28456217407305291469…86020435466753507521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.691 × 10¹²⁷(128-digit number)

56912434814610582939…72040870933507015041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.138 × 10¹²⁸(129-digit number)

11382486962922116587…44081741867014030081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.276 × 10¹²⁸(129-digit number)

22764973925844233175…88163483734028060161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.552 × 10¹²⁸(129-digit number)

45529947851688466351…76326967468056120321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.105 × 10¹²⁸(129-digit number)

91059895703376932702…52653934936112240641

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer