Block #285,625

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/30/2013, 1:43:49 PM · Difficulty 9.9846 · 6,506,542 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

fa18c868925b13296b269302c840864fb3d03b7a768fc006ec756f219bb252a7

View on Chainz ↗

Height

#285,625

Difficulty

9.984563

Transactions

Size

1004 B

Version

Bits

09fc0c4e

Nonce

100,482

Timestamp

11/30/2013, 1:43:49 PM

Confirmations

6,506,542

Merkle Root

b300d8d6f0217275b3e4d13fe2e4119ff735035f78524d8be1571221956f2989

Transactions (1)

Coinbaseb300d8d6f02172…571221956f2989

1 in → 25 out10.0200 XPM913 B

AcP9aGkN…9c7TeeiQ AXydriH2…RUoBRJjB AWxMqAjD…jNai1Anq ANuKx9Ke…wm7nrBRq AHuJ9wYh…BGmgHrKZ

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.

3.731 × 10⁹⁶(97-digit number)

37316413675040236297…13416179804052382401

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

3.731 × 10⁹⁶(97-digit number)

37316413675040236297…13416179804052382401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.463 × 10⁹⁶(97-digit number)

74632827350080472595…26832359608104764801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.492 × 10⁹⁷(98-digit number)

14926565470016094519…53664719216209529601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.985 × 10⁹⁷(98-digit number)

29853130940032189038…07329438432419059201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.970 × 10⁹⁷(98-digit number)

59706261880064378076…14658876864838118401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.194 × 10⁹⁸(99-digit number)

11941252376012875615…29317753729676236801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.388 × 10⁹⁸(99-digit number)

23882504752025751230…58635507459352473601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.776 × 10⁹⁸(99-digit number)

47765009504051502461…17271014918704947201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.553 × 10⁹⁸(99-digit number)

95530019008103004922…34542029837409894401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.910 × 10⁹⁹(100-digit number)

19106003801620600984…69084059674819788801

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