Block #201,859

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/9/2013, 9:11:06 PM · Difficulty 9.8935 · 6,592,328 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

22e29c7863b9cd22628c8f2ad5c83ea0ba35588bb36867f454d79d7a33266d74

View on Chainz ↗

Height

#201,859

Difficulty

9.893465

Transactions

Size

199 B

Version

Bits

09e4ba23

Nonce

30,191

Timestamp

10/9/2013, 9:11:06 PM

Confirmations

6,592,328

Merkle Root

76c99bd8a871f2a73afb020f28584f42a56b82306f3d18eaf63fdfe53949ddac

Transactions (1)

Coinbase76c99bd8a871f2…3fdfe53949ddac

1 in → 1 out10.2000 XPM109 B

AK9vVy2j…niNoc5U8

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.

1.353 × 10⁹⁴(95-digit number)

13530995639704606330…32331230315065891841

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

1.353 × 10⁹⁴(95-digit number)

13530995639704606330…32331230315065891841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.706 × 10⁹⁴(95-digit number)

27061991279409212661…64662460630131783681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.412 × 10⁹⁴(95-digit number)

54123982558818425322…29324921260263567361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.082 × 10⁹⁵(96-digit number)

10824796511763685064…58649842520527134721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.164 × 10⁹⁵(96-digit number)

21649593023527370129…17299685041054269441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.329 × 10⁹⁵(96-digit number)

43299186047054740258…34599370082108538881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.659 × 10⁹⁵(96-digit number)

86598372094109480516…69198740164217077761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.731 × 10⁹⁶(97-digit number)

17319674418821896103…38397480328434155521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.463 × 10⁹⁶(97-digit number)

34639348837643792206…76794960656868311041

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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