Block #283,774

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/29/2013, 9:12:38 PM · Difficulty 9.9816 · 6,508,128 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

710a79800840bf8507eac6bf50e4370692045b1ea93f5a7e457c102b46cd5f33

View on Chainz ↗

Height

#283,774

Difficulty

9.981623

Transactions

Size

1.42 KB

Version

Bits

09fb4bac

Nonce

613

Timestamp

11/29/2013, 9:12:38 PM

Confirmations

6,508,128

Merkle Root

ce73d0eb086184faa5d448b982c640fc76ac80b8d53e2a532672284e8ba3f093

Transactions (2)

Coinbasee35cbfa6a5821e…f971a36542375d

1 in → 1 out10.0400 XPM109 B

AWfxptAe…o52CtvRh

f9aa9f1f440e42…05e589ca6c7b11

8 in → 2 out74.6678 XPM1.23 KB

AcLCYHkJ…AHL44GHw AYvzdPBW…rCYhot7T

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.

7.532 × 10⁹⁵(96-digit number)

75320134628061191124…05052747590797625121

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

7.532 × 10⁹⁵(96-digit number)

75320134628061191124…05052747590797625121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.506 × 10⁹⁶(97-digit number)

15064026925612238224…10105495181595250241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.012 × 10⁹⁶(97-digit number)

30128053851224476449…20210990363190500481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.025 × 10⁹⁶(97-digit number)

60256107702448952899…40421980726381000961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.205 × 10⁹⁷(98-digit number)

12051221540489790579…80843961452762001921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.410 × 10⁹⁷(98-digit number)

24102443080979581159…61687922905524003841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.820 × 10⁹⁷(98-digit number)

48204886161959162319…23375845811048007681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.640 × 10⁹⁷(98-digit number)

96409772323918324639…46751691622096015361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.928 × 10⁹⁸(99-digit number)

19281954464783664927…93503383244192030721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.856 × 10⁹⁸(99-digit number)

38563908929567329855…87006766488384061441

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