Block #108,045

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/9/2013, 8:07:52 PM · Difficulty 9.6402 · 6,683,110 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f2befbb855c66cfa95c709fc3fe0ed5effaa93407e23825725bf9295133aaba8

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Height

#108,045

Difficulty

9.640210

Transactions

Size

201 B

Version

Bits

09a3e4d1

Nonce

67,278

Timestamp

8/9/2013, 8:07:52 PM

Confirmations

6,683,110

Merkle Root

3d7b8849f5052bee72fc218a786d29cd7602265ac0dade327cccb144545e3cd8

Transactions (1)

Coinbase3d7b8849f5052b…ccb144545e3cd8

1 in → 1 out10.7400 XPM109 B

AWuDuxGX…tLDpHWp7

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.

2.585 × 10¹⁰⁰(101-digit number)

25852284211064876629…52327110852895943751

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

2.585 × 10¹⁰⁰(101-digit number)

25852284211064876629…52327110852895943751

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.170 × 10¹⁰⁰(101-digit number)

51704568422129753259…04654221705791887501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.034 × 10¹⁰¹(102-digit number)

10340913684425950651…09308443411583775001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.068 × 10¹⁰¹(102-digit number)

20681827368851901303…18616886823167550001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.136 × 10¹⁰¹(102-digit number)

41363654737703802607…37233773646335100001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.272 × 10¹⁰¹(102-digit number)

82727309475407605215…74467547292670200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.654 × 10¹⁰²(103-digit number)

16545461895081521043…48935094585340400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.309 × 10¹⁰²(103-digit number)

33090923790163042086…97870189170680800001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.618 × 10¹⁰²(103-digit number)

66181847580326084172…95740378341361600001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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