Block #1,102,687

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/13/2015, 12:13:05 PM · Difficulty 10.7559 · 5,691,482 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

cb259f26620aaec6180249523c5811bc7708ea6685958b543c1d509792bf4e56

View on Chainz ↗

Height

#1,102,687

Difficulty

10.755857

Transactions

Size

539 B

Version

Bits

0ac17fda

Nonce

702,679,654

Timestamp

6/13/2015, 12:13:05 PM

Confirmations

5,691,482

Merkle Root

41aa90974319a3ae8e1495db9e0f29181eec93adf68616913610b3e3d5b2f657

Transactions (2)

Coinbasee8ddcd48bbcaef…bcd5b3243f88d1

1 in → 1 out8.6400 XPM109 B

AKy3U9qJ…prooStbv

6b2708edc44ac1…84a8fd10a823f2

2 in → 1 out999.9901 XPM340 B

AQ3SuyCM…AmNvneTb

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.

3.082 × 10⁹³(94-digit number)

30827055642057537124…52803165594486170881

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

3.082 × 10⁹³(94-digit number)

30827055642057537124…52803165594486170881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.165 × 10⁹³(94-digit number)

61654111284115074249…05606331188972341761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.233 × 10⁹⁴(95-digit number)

12330822256823014849…11212662377944683521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.466 × 10⁹⁴(95-digit number)

24661644513646029699…22425324755889367041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.932 × 10⁹⁴(95-digit number)

49323289027292059399…44850649511778734081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.864 × 10⁹⁴(95-digit number)

98646578054584118799…89701299023557468161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.972 × 10⁹⁵(96-digit number)

19729315610916823759…79402598047114936321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.945 × 10⁹⁵(96-digit number)

39458631221833647519…58805196094229872641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.891 × 10⁹⁵(96-digit number)

78917262443667295039…17610392188459745281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.578 × 10⁹⁶(97-digit number)

15783452488733459007…35220784376919490561

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer