Block #1,091,437

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/5/2015, 10:39:17 PM · Difficulty 10.7373 · 5,707,856 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

25b0b9abdd234fbfd9f87e27e59e06b71a9628270fb9aff900124f56ef4ce4c4

View on Chainz ↗

Height

#1,091,437

Difficulty

10.737335

Transactions

Size

243 B

Version

Bits

0abcc201

Nonce

476,126,179

Timestamp

6/5/2015, 10:39:17 PM

Confirmations

5,707,856

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

95099729adcedaeebcbc1f21b9643c15c6bd272e2e8ba2148f95b5f0dfcdfda1

Transactions (1)

Coinbase95099729adceda…95b5f0dfcdfda1

1 in → 2 out8.6600 XPM152 B

APGBorYS…QnZrTNSi ALPu3s2c…EJXLjVFh

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.

1.885 × 10⁹⁷(98-digit number)

18855695037091718223…72624888340562078719

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

1.885 × 10⁹⁷(98-digit number)

18855695037091718223…72624888340562078719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.771 × 10⁹⁷(98-digit number)

37711390074183436447…45249776681124157439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.542 × 10⁹⁷(98-digit number)

75422780148366872895…90499553362248314879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.508 × 10⁹⁸(99-digit number)

15084556029673374579…80999106724496629759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.016 × 10⁹⁸(99-digit number)

30169112059346749158…61998213448993259519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.033 × 10⁹⁸(99-digit number)

60338224118693498316…23996426897986519039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.206 × 10⁹⁹(100-digit number)

12067644823738699663…47992853795973038079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.413 × 10⁹⁹(100-digit number)

24135289647477399326…95985707591946076159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.827 × 10⁹⁹(100-digit number)

48270579294954798653…91971415183892152319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.654 × 10⁹⁹(100-digit number)

96541158589909597306…83942830367784304639

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