Block #433,547

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2014, 3:55:11 PM · Difficulty 10.3455 · 6,361,899 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

10086c303013af58843c8e6c1f84d85208265fb170bb4ed7931ca41b2f36281a

View on Chainz ↗

Height

#433,547

Difficulty

10.345479

Transactions

Size

1.05 KB

Version

Bits

0a58714d

Nonce

15,419

Timestamp

3/7/2014, 3:55:11 PM

Confirmations

6,361,899

Mined by

⛏️ P2SHAJVwetHHftcJ76YGAvnvdJSJz67RSvsSkW

Merkle Root

cab8ba4f586ea7a4d5ea794739f5ec866602b56a0f2ef3391c937b5a8aac8ed6

Transactions (2)

Coinbaseedbc92cd9884eb…e5ad0db9814874

1 in → 1 out9.3400 XPM109 B

AJVwetHH…7RSvsSkW

d57fc3fd941a78…4471d92e975843

4 in → 12 out37.3600 XPM876 B

ANVQgy2y…heyFibjn ANFbFgck…gYuJJWxY ATYHB6jH…M8vFw7Cc AdTtZYv4…mEzssnpx AezqbyYF…jVCXwRyN

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.

1.554 × 10⁹³(94-digit number)

15549235837605933188…61646307681703914671

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

1.554 × 10⁹³(94-digit number)

15549235837605933188…61646307681703914671

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.109 × 10⁹³(94-digit number)

31098471675211866376…23292615363407829341

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.219 × 10⁹³(94-digit number)

62196943350423732752…46585230726815658681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.243 × 10⁹⁴(95-digit number)

12439388670084746550…93170461453631317361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.487 × 10⁹⁴(95-digit number)

24878777340169493101…86340922907262634721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.975 × 10⁹⁴(95-digit number)

49757554680338986202…72681845814525269441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.951 × 10⁹⁴(95-digit number)

99515109360677972404…45363691629050538881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.990 × 10⁹⁵(96-digit number)

19903021872135594480…90727383258101077761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.980 × 10⁹⁵(96-digit number)

39806043744271188961…81454766516202155521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.961 × 10⁹⁵(96-digit number)

79612087488542377923…62909533032404311041

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