Block #261,790

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/16/2013, 4:00:16 AM · Difficulty 9.9708 · 6,547,860 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5b5db07f42f6516eb8f3ef17c2d58f9ccbaccb5ed2e5963dd6481373eed82487

View on Chainz ↗

Height

#261,790

Difficulty

9.970755

Transactions

Size

1.84 KB

Version

Bits

09f88364

Nonce

953,777

Timestamp

11/16/2013, 4:00:16 AM

Confirmations

6,547,860

Mined by

⛏️ aRALd5yTY2V1TpjhCtBduYkduB11vgfAFVPZ

Merkle Root

52ae6546a6e99b358ef6326b105aab47009a83b0c38dfedad7acf479560048d2

Transactions (1)

Coinbase52ae6546a6e99b…acf479560048d2

1 in → 51 out10.0200 XPM1.75 KB

ALd5yTY2…vgfAFVPZ AFqKfjez…qX9Ace3g APH8rV6F…heb1HF2Z AQtzUSwq…htAuF3yC AToj6KA9…ioTFgSxT

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.

4.511 × 10⁹¹(92-digit number)

45113637649245686745…04952786365271753131

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

4.511 × 10⁹¹(92-digit number)

45113637649245686745…04952786365271753131

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.022 × 10⁹¹(92-digit number)

90227275298491373490…09905572730543506261

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.804 × 10⁹²(93-digit number)

18045455059698274698…19811145461087012521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.609 × 10⁹²(93-digit number)

36090910119396549396…39622290922174025041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.218 × 10⁹²(93-digit number)

72181820238793098792…79244581844348050081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.443 × 10⁹³(94-digit number)

14436364047758619758…58489163688696100161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.887 × 10⁹³(94-digit number)

28872728095517239516…16978327377392200321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.774 × 10⁹³(94-digit number)

57745456191034479033…33956654754784400641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.154 × 10⁹⁴(95-digit number)

11549091238206895806…67913309509568801281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.309 × 10⁹⁴(95-digit number)

23098182476413791613…35826619019137602561

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 #261,790

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