Block #1,395,499

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/2/2016, 5:07:11 AM · Difficulty 10.8115 · 5,413,385 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8fd77ff97b43ae3617014d9a06ee905f36237b9176bf4da84e7ec26f3ea4e396

View on Chainz ↗

Height

#1,395,499

Difficulty

10.811492

Transactions

Size

237 B

Version

Bits

0acfbdec

Nonce

16,922

Timestamp

1/2/2016, 5:07:11 AM

Confirmations

5,413,385

Mined by

⛏️ P2SHAJCcxnuA2gFsc6HJAVptkiMzbSBeS8SCFB

Merkle Root

e59e0b4cbb935927702f4482404ed440b3a9c519d85afaca39cfa0025ab9595c

Transactions (1)

Coinbasee59e0b4cbb9359…cfa0025ab9595c

1 in → 2 out8.5400 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.

2.073 × 10⁹⁹(100-digit number)

20736678460473368530…69553282657435339521

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

2.073 × 10⁹⁹(100-digit number)

20736678460473368530…69553282657435339521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.147 × 10⁹⁹(100-digit number)

41473356920946737061…39106565314870679041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.294 × 10⁹⁹(100-digit number)

82946713841893474123…78213130629741358081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.658 × 10¹⁰⁰(101-digit number)

16589342768378694824…56426261259482716161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.317 × 10¹⁰⁰(101-digit number)

33178685536757389649…12852522518965432321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.635 × 10¹⁰⁰(101-digit number)

66357371073514779298…25705045037930864641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.327 × 10¹⁰¹(102-digit number)

13271474214702955859…51410090075861729281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.654 × 10¹⁰¹(102-digit number)

26542948429405911719…02820180151723458561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.308 × 10¹⁰¹(102-digit number)

53085896858811823438…05640360303446917121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.061 × 10¹⁰²(103-digit number)

10617179371762364687…11280720606893834241

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

Block #1,395,499

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