Block #319,327

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/18/2013, 11:00:21 PM · Difficulty 10.1674 · 6,489,692 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d4dd5c3bb22b1554c716cc143b57b3149c0bc918fcb3f6d0ab9ee9ffdc5a7da7

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Height

#319,327

Difficulty

10.167450

Transactions

Size

202 B

Version

Bits

0a2addfe

Nonce

499,677

Timestamp

12/18/2013, 11:00:21 PM

Confirmations

6,489,692

Mined by

⛏️ P2SHAUvnWbpfCUyVyWBgdFNjQdztf1c9d1JDFv

Merkle Root

784ab5fec95da3077a12e4fee68d9615b951e4ccf1799660f52637f87ae4af48

Transactions (1)

Coinbase784ab5fec95da3…2637f87ae4af48

1 in → 1 out9.6600 XPM109 B

AUvnWbpf…c9d1JDFv

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.

1.135 × 10¹⁰²(103-digit number)

11358704998336705462…68867256543350944001

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

1.135 × 10¹⁰²(103-digit number)

11358704998336705462…68867256543350944001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.271 × 10¹⁰²(103-digit number)

22717409996673410925…37734513086701888001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.543 × 10¹⁰²(103-digit number)

45434819993346821850…75469026173403776001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.086 × 10¹⁰²(103-digit number)

90869639986693643700…50938052346807552001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.817 × 10¹⁰³(104-digit number)

18173927997338728740…01876104693615104001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.634 × 10¹⁰³(104-digit number)

36347855994677457480…03752209387230208001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.269 × 10¹⁰³(104-digit number)

72695711989354914960…07504418774460416001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.453 × 10¹⁰⁴(105-digit number)

14539142397870982992…15008837548920832001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.907 × 10¹⁰⁴(105-digit number)

29078284795741965984…30017675097841664001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.815 × 10¹⁰⁴(105-digit number)

58156569591483931968…60035350195683328001

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

Block #319,327

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