Block #364,602

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2014, 4:45:05 AM · Difficulty 10.4206 · 6,461,585 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6bfcadcb5f0fd6cc922f1085a53ee7ae2a00ac35e37f8d236c832ab0327df015

View on Chainz ↗

Height

#364,602

Difficulty

10.420588

Transactions

Size

212 B

Version

Bits

0a6babb0

Nonce

1,090,221

Timestamp

1/18/2014, 4:45:05 AM

Confirmations

6,461,585

Mined by

⛏️ P2SHAW6FdqAF2QFTdoj8WBd1FEKDKLmbtgXE2r

Merkle Root

f17dfc2d7e72ae546c130f4842f6a4a05ff1422a4da5768692a502f1ed8041d2

Transactions (1)

Coinbasef17dfc2d7e72ae…a502f1ed8041d2

1 in → 1 out9.1900 XPM118 B

AW6FdqAF…mbtgXE2r

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.

2.170 × 10¹⁰³(104-digit number)

21706552607342040566…36458617219653304321

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

2.170 × 10¹⁰³(104-digit number)

21706552607342040566…36458617219653304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.341 × 10¹⁰³(104-digit number)

43413105214684081133…72917234439306608641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.682 × 10¹⁰³(104-digit number)

86826210429368162267…45834468878613217281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.736 × 10¹⁰⁴(105-digit number)

17365242085873632453…91668937757226434561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.473 × 10¹⁰⁴(105-digit number)

34730484171747264907…83337875514452869121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.946 × 10¹⁰⁴(105-digit number)

69460968343494529814…66675751028905738241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.389 × 10¹⁰⁵(106-digit number)

13892193668698905962…33351502057811476481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.778 × 10¹⁰⁵(106-digit number)

27784387337397811925…66703004115622952961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.556 × 10¹⁰⁵(106-digit number)

55568774674795623851…33406008231245905921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.111 × 10¹⁰⁶(107-digit number)

11113754934959124770…66812016462491811841

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 #364,602

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