Block #60,925

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 10:34:55 AM · Difficulty 8.9712 · 6,730,062 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a77ac9319f4e9c9020ae303246c17a1c901abbe0de0c0f6d8135f6a7cc1715e2

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Height

#60,925

Difficulty

8.971182

Transactions

Size

203 B

Version

Bits

08f89f60

Nonce

544

Timestamp

7/18/2013, 10:34:55 AM

Confirmations

6,730,062

Merkle Root

429887e2287ddf6ac760f473e0237376525abc2eac9df001e13746c229242592

Transactions (1)

Coinbase429887e2287ddf…3746c229242592

1 in → 1 out12.4100 XPM110 B

AK1JUKWL…oPR4rN5o

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.

1.140 × 10¹⁰¹(102-digit number)

11402736033209001385…76716916894384391201

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

1.140 × 10¹⁰¹(102-digit number)

11402736033209001385…76716916894384391201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.280 × 10¹⁰¹(102-digit number)

22805472066418002770…53433833788768782401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.561 × 10¹⁰¹(102-digit number)

45610944132836005540…06867667577537564801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.122 × 10¹⁰¹(102-digit number)

91221888265672011081…13735335155075129601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.824 × 10¹⁰²(103-digit number)

18244377653134402216…27470670310150259201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.648 × 10¹⁰²(103-digit number)

36488755306268804432…54941340620300518401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.297 × 10¹⁰²(103-digit number)

72977510612537608865…09882681240601036801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.459 × 10¹⁰³(104-digit number)

14595502122507521773…19765362481202073601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.919 × 10¹⁰³(104-digit number)

29191004245015043546…39530724962404147201

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×2−1 →

2^9 × origin + 1

5.838 × 10¹⁰³(104-digit number)

58382008490030087092…79061449924808294401

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