Block #52,959

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 12:58:47 PM · Difficulty 8.9182 · 6,742,090 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3c23aac7fd6a19d19c27f7ac7ff6e62a4b32bffb68f4cb17f1cd5dcb9ba516fa

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Height

#52,959

Difficulty

8.918225

Transactions

Size

15.31 KB

Version

Bits

08eb10cd

Nonce

334

Timestamp

7/16/2013, 12:58:47 PM

Confirmations

6,742,090

Mined by

⛏️ P2SHAXCdZYjb81W335y8a1DGFfctbGnwhpq2g9

Merkle Root

b6ae0a570ce439cb1be6edba7710d1d527419987614888c7674ce121257844eb

Transactions (2)

Coinbasede944b67b8e6ad…4a5dd489c0420a

1 in → 1 out12.7200 XPM110 B

AXCdZYjb…nwhpq2g9

deb6531cc65990…bb47cdc6f2259c

135 in → 2 out1720.1300 XPM15.11 KB

AHdhnVHa…xHqEjaxD AMmUy3x3…qPezWtyV

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.

1.490 × 10¹¹¹(112-digit number)

14904782674002864335…06609398524169325731

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

1.490 × 10¹¹¹(112-digit number)

14904782674002864335…06609398524169325731

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.980 × 10¹¹¹(112-digit number)

29809565348005728670…13218797048338651461

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.961 × 10¹¹¹(112-digit number)

59619130696011457340…26437594096677302921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.192 × 10¹¹²(113-digit number)

11923826139202291468…52875188193354605841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.384 × 10¹¹²(113-digit number)

23847652278404582936…05750376386709211681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.769 × 10¹¹²(113-digit number)

47695304556809165872…11500752773418423361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.539 × 10¹¹²(113-digit number)

95390609113618331744…23001505546836846721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.907 × 10¹¹³(114-digit number)

19078121822723666348…46003011093673693441

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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