Block #263,101

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/17/2013, 11:58:15 AM · Difficulty 9.9670 · 6,540,637 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d54a4bea11f42d5f8316bc75780d9fef154048ec47165a45bfaed2ae6406b7b9

View on Chainz ↗

Height

#263,101

Difficulty

9.967042

Transactions

Size

1.88 KB

Version

Bits

09f79010

Nonce

31,396

Timestamp

11/17/2013, 11:58:15 AM

Confirmations

6,540,637

Mined by

⛏️ aR@AHUMdCV54x18CaET8oCChA41wTeXnCsijo

Merkle Root

a8ca3f9ab8e41915e4ab1e38dc1bf353b41ea214c891c47ab0925b3f3fa46ac3

Transactions (1)

Coinbasea8ca3f9ab8e419…925b3f3fa46ac3

1 in → 52 out10.0300 XPM1.79 KB

AHUMdCV5…eXnCsijo AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs

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.

3.038 × 10⁹³(94-digit number)

30389227187275638923…70640705417750480801

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

3.038 × 10⁹³(94-digit number)

30389227187275638923…70640705417750480801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.077 × 10⁹³(94-digit number)

60778454374551277847…41281410835500961601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.215 × 10⁹⁴(95-digit number)

12155690874910255569…82562821671001923201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.431 × 10⁹⁴(95-digit number)

24311381749820511138…65125643342003846401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.862 × 10⁹⁴(95-digit number)

48622763499641022277…30251286684007692801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.724 × 10⁹⁴(95-digit number)

97245526999282044555…60502573368015385601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.944 × 10⁹⁵(96-digit number)

19449105399856408911…21005146736030771201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.889 × 10⁹⁵(96-digit number)

38898210799712817822…42010293472061542401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.779 × 10⁹⁵(96-digit number)

77796421599425635644…84020586944123084801

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