Block #60,539

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 8:30:17 AM · Difficulty 8.9696 · 6,729,212 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

50780d52f1309f413adea37a5296ba3492410c3868348d8b103cc84aafba142e

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Height

#60,539

Difficulty

8.969640

Transactions

Size

726 B

Version

Bits

08f83a56

Nonce

1,085

Timestamp

7/18/2013, 8:30:17 AM

Confirmations

6,729,212

Merkle Root

bc0e0b06103c309c7f27c6af057f5c1102ff687d37d0f44039d3fa29f6fad248

Transactions (2)

Coinbasee5750315dabfcf…c32a278eab6f87

1 in → 1 out12.4200 XPM110 B

AQKr7Xjz…hui9hXz5

6045569ce51b04…c20b70ab14011b

3 in → 2 out136.1801 XPM520 B

AL5iHwkH…YGkGxDZC AJ8PJJ4M…qFmKnwRS

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.

8.914 × 10¹⁰⁸(109-digit number)

89149317391677235752…63991628105058914601

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

8.914 × 10¹⁰⁸(109-digit number)

89149317391677235752…63991628105058914601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.782 × 10¹⁰⁹(110-digit number)

17829863478335447150…27983256210117829201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.565 × 10¹⁰⁹(110-digit number)

35659726956670894301…55966512420235658401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.131 × 10¹⁰⁹(110-digit number)

71319453913341788602…11933024840471316801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.426 × 10¹¹⁰(111-digit number)

14263890782668357720…23866049680942633601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.852 × 10¹¹⁰(111-digit number)

28527781565336715440…47732099361885267201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.705 × 10¹¹⁰(111-digit number)

57055563130673430881…95464198723770534401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.141 × 10¹¹¹(112-digit number)

11411112626134686176…90928397447541068801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.282 × 10¹¹¹(112-digit number)

22822225252269372352…81856794895082137601

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