Block #250,508

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/8/2013, 1:12:31 PM · Difficulty 9.9684 · 6,560,228 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ad76b0a363442889d86c27b77dd4132796b99d53ae04369a48faa9d36c891608

View on Chainz ↗

Height

#250,508

Difficulty

9.968439

Transactions

Size

1.84 KB

Version

Bits

09f7eb9f

Nonce

6,224

Timestamp

11/8/2013, 1:12:31 PM

Confirmations

6,560,228

Mined by

⛏️ aR|=AaSot6r4yv2wY1rm3V3SJd5frtDjoWHEUX

Merkle Root

7d407d9d81ca74710561ba0f0f513dbe96cd152c0a1159c2266d2370c58c9800

Transactions (1)

Coinbase7d407d9d81ca74…6d2370c58c9800

1 in → 51 out10.0296 XPM1.75 KB

AaSot6r4…DjoWHEUX AFqKfjez…qX9Ace3g AabHNb1B…GRoingRy ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

1.553 × 10⁹³(94-digit number)

15539371161286772914…64888149682861113319

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

1.553 × 10⁹³(94-digit number)

15539371161286772914…64888149682861113319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.107 × 10⁹³(94-digit number)

31078742322573545829…29776299365722226639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.215 × 10⁹³(94-digit number)

62157484645147091658…59552598731444453279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.243 × 10⁹⁴(95-digit number)

12431496929029418331…19105197462888906559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.486 × 10⁹⁴(95-digit number)

24862993858058836663…38210394925777813119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.972 × 10⁹⁴(95-digit number)

49725987716117673326…76420789851555626239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.945 × 10⁹⁴(95-digit number)

99451975432235346653…52841579703111252479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.989 × 10⁹⁵(96-digit number)

19890395086447069330…05683159406222504959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.978 × 10⁹⁵(96-digit number)

39780790172894138661…11366318812445009919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.956 × 10⁹⁵(96-digit number)

79561580345788277322…22732637624890019839

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #250,508

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