Block #258,646

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/13/2013, 4:32:04 AM · Difficulty 9.9766 · 6,537,049 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0fdb750ae3b33886c0d799f81ab7176779eedf51ecd9b4e38c9d6a60bde7288d

View on Chainz ↗

Height

#258,646

Difficulty

9.976583

Transactions

Size

2.11 KB

Version

Bits

09fa0150

Nonce

64,719

Timestamp

11/13/2013, 4:32:04 AM

Confirmations

6,537,049

Mined by

⛏️ VaRANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

d50de7e4241dbc0a9bf3163903a0b111b7297f488eafca19f9967b96316d340c

Transactions (1)

Coinbased50de7e4241dbc…967b96316d340c

1 in → 59 out9.9960 XPM2.02 KB

ANo4YY1x…vnsPRDSU AWstywZj…GM4bUf73 AQtzUSwq…htAuF3yC AHeVugNM…1STQZ4jA APZy8y6E…QZaGQjfp

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.

2.946 × 10⁹⁵(96-digit number)

29468329410312455508…58021551047189308161

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

2.946 × 10⁹⁵(96-digit number)

29468329410312455508…58021551047189308161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.893 × 10⁹⁵(96-digit number)

58936658820624911016…16043102094378616321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.178 × 10⁹⁶(97-digit number)

11787331764124982203…32086204188757232641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.357 × 10⁹⁶(97-digit number)

23574663528249964406…64172408377514465281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.714 × 10⁹⁶(97-digit number)

47149327056499928813…28344816755028930561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.429 × 10⁹⁶(97-digit number)

94298654112999857626…56689633510057861121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.885 × 10⁹⁷(98-digit number)

18859730822599971525…13379267020115722241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.771 × 10⁹⁷(98-digit number)

37719461645199943050…26758534040231444481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.543 × 10⁹⁷(98-digit number)

75438923290399886101…53517068080462888961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.508 × 10⁹⁸(99-digit number)

15087784658079977220…07034136160925777921

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