Block #276,141

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 1:14:40 AM · Difficulty 9.9624 · 6,516,024 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1f354c2a632c0110de93241d932a10187abab3c10dc7b2f121727c3f39408d00

View on Chainz ↗

Height

#276,141

Difficulty

9.962448

Transactions

Size

1.14 KB

Version

Bits

09f662f6

Nonce

100,491

Timestamp

11/27/2013, 1:14:40 AM

Confirmations

6,516,024

Merkle Root

e8263d4e5bf1a2e41a2f26b5efb014dfc9a0c56f1c0cd3fb06d4dfc0c0e9402a

Transactions (1)

Coinbasee8263d4e5bf1a2…d4dfc0c0e9402a

1 in → 30 out10.0400 XPM1.06 KB

AJzWx2VD…j4ZSMit5 AVss9H5F…zXhyMijY AN63YyQR…1tfe566A AUQHP8oJ…LpEKyRph AZxfJPuB…prEg2B2i

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.

3.344 × 10⁹²(93-digit number)

33447222355898146571…03156688190465511199

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

3.344 × 10⁹²(93-digit number)

33447222355898146571…03156688190465511199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.689 × 10⁹²(93-digit number)

66894444711796293142…06313376380931022399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.337 × 10⁹³(94-digit number)

13378888942359258628…12626752761862044799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.675 × 10⁹³(94-digit number)

26757777884718517256…25253505523724089599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.351 × 10⁹³(94-digit number)

53515555769437034513…50507011047448179199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.070 × 10⁹⁴(95-digit number)

10703111153887406902…01014022094896358399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.140 × 10⁹⁴(95-digit number)

21406222307774813805…02028044189792716799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.281 × 10⁹⁴(95-digit number)

42812444615549627611…04056088379585433599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.562 × 10⁹⁴(95-digit number)

85624889231099255222…08112176759170867199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.712 × 10⁹⁵(96-digit number)

17124977846219851044…16224353518341734399

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