Block #120,912

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/17/2013, 11:48:53 AM · Difficulty 9.7512 · 6,670,029 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d16d89897895d650013daed4ec9578c3e2e739f664315d27547cf8c7db8e4828

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Height

#120,912

Difficulty

9.751198

Transactions

Size

201 B

Version

Bits

09c04e8b

Nonce

10,503

Timestamp

8/17/2013, 11:48:53 AM

Confirmations

6,670,029

Merkle Root

bc67db70832caccf4cc0559c75770596add94d98acfc0a4a8dbd4ba8ed229ffb

Transactions (1)

Coinbasebc67db70832cac…bd4ba8ed229ffb

1 in → 1 out10.5000 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.

2.498 × 10¹⁰⁰(101-digit number)

24981234040261629989…70907746293749838101

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

2.498 × 10¹⁰⁰(101-digit number)

24981234040261629989…70907746293749838101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.996 × 10¹⁰⁰(101-digit number)

49962468080523259979…41815492587499676201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.992 × 10¹⁰⁰(101-digit number)

99924936161046519958…83630985174999352401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.998 × 10¹⁰¹(102-digit number)

19984987232209303991…67261970349998704801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.996 × 10¹⁰¹(102-digit number)

39969974464418607983…34523940699997409601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.993 × 10¹⁰¹(102-digit number)

79939948928837215966…69047881399994819201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.598 × 10¹⁰²(103-digit number)

15987989785767443193…38095762799989638401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.197 × 10¹⁰²(103-digit number)

31975979571534886386…76191525599979276801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.395 × 10¹⁰²(103-digit number)

63951959143069772773…52383051199958553601

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