Block #190,090

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/2/2013, 6:17:07 AM · Difficulty 9.8738 · 6,605,205 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fc2488cf73375da88eb6a8f036df7901ad904acc7e99b5e5d691e8dc1e2ee73c

View on Chainz ↗

Height

#190,090

Difficulty

9.873802

Transactions

Size

3.63 KB

Version

Bits

09dfb178

Nonce

1,164,960,322

Timestamp

10/2/2013, 6:17:07 AM

Confirmations

6,605,205

Mined by

⛏️ RKyAJBVSqB9CkWZf5mKx3aw422CzJnso7kkMM

Merkle Root

1bd96a3acc73d0f416659ba35f017f14f4754e112074a683ab8f6c78657914c4

Transactions (1)

Coinbase1bd96a3acc73d0…8f6c78657914c4

1 in → 105 out10.2100 XPM3.55 KB

AJBVSqB9…nso7kkMM ATeGzPEb…fEYhKxfs AZ4gvP32…ukKsCiYr AQU8M5oq…HrH12dei AakGxn9J…d7mTfZVK

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.

3.598 × 10⁹⁴(95-digit number)

35985897914524935655…42482134500612655999

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

3.598 × 10⁹⁴(95-digit number)

35985897914524935655…42482134500612655999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.197 × 10⁹⁴(95-digit number)

71971795829049871311…84964269001225311999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.439 × 10⁹⁵(96-digit number)

14394359165809974262…69928538002450623999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.878 × 10⁹⁵(96-digit number)

28788718331619948524…39857076004901247999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.757 × 10⁹⁵(96-digit number)

57577436663239897049…79714152009802495999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.151 × 10⁹⁶(97-digit number)

11515487332647979409…59428304019604991999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.303 × 10⁹⁶(97-digit number)

23030974665295958819…18856608039209983999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.606 × 10⁹⁶(97-digit number)

46061949330591917639…37713216078419967999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.212 × 10⁹⁶(97-digit number)

92123898661183835279…75426432156839935999

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer