Block #1,149,413

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/10/2015, 9:57:57 PM · Difficulty 10.9432 · 5,654,094 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9e5150b7236380e405dc85f9181edf577cf27527593b3e5dec76c52131ddd48d

View on Chainz ↗

Height

#1,149,413

Difficulty

10.943215

Transactions

Size

236 B

Version

Bits

0af17688

Nonce

39,723

Timestamp

7/10/2015, 9:57:57 PM

Confirmations

5,654,094

Mined by

⛏️ P2SHAJCcxnuA2gFsc6HJAVptkiMzbSBeS8SCFB

Merkle Root

a050679e928677c2831fe772ebe4416f9ef7c35416e904f904ac44b24402cbff

Transactions (1)

Coinbasea050679e928677…ac44b24402cbff

1 in → 2 out8.3400 XPM145 B

AJCcxnuA…BeS8SCFB Ac7DbgrK…XDMazkvn

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.

7.801 × 10⁹⁶(97-digit number)

78014796699526308033…14964214931489721599

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

7.801 × 10⁹⁶(97-digit number)

78014796699526308033…14964214931489721599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.560 × 10⁹⁷(98-digit number)

15602959339905261606…29928429862979443199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.120 × 10⁹⁷(98-digit number)

31205918679810523213…59856859725958886399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.241 × 10⁹⁷(98-digit number)

62411837359621046426…19713719451917772799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.248 × 10⁹⁸(99-digit number)

12482367471924209285…39427438903835545599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.496 × 10⁹⁸(99-digit number)

24964734943848418570…78854877807671091199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.992 × 10⁹⁸(99-digit number)

49929469887696837141…57709755615342182399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.985 × 10⁹⁸(99-digit number)

99858939775393674282…15419511230684364799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.997 × 10⁹⁹(100-digit number)

19971787955078734856…30839022461368729599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.994 × 10⁹⁹(100-digit number)

39943575910157469713…61678044922737459199

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