Block #74,096

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 9:26:24 AM · Difficulty 8.9953 · 6,715,874 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dda5e2d0ba89dfb6742be17c1dd57bb9428d2623d686a2ca55620b5eb08fd4fb

View on Chainz ↗

Height

#74,096

Difficulty

8.995282

Transactions

Size

1.80 KB

Version

Bits

08fecacf

Nonce

239

Timestamp

7/21/2013, 9:26:24 AM

Confirmations

6,715,874

Merkle Root

1f1a12dbe1ca28f8172d0c69b63a673120f52e5f77bfe310f54c9259f0f5282c

Transactions (3)

Coinbasef72f2c852844bb…a5086f98739185

1 in → 1 out12.3700 XPM110 B

AVQxbFsH…KG2vYXbz

eec444ecf64a22…db465ccf612d28

11 in → 2 out123.5110 XPM1.33 KB

AZG4fqQE…MKJTpZdP AdNeXXkk…QpfXAns4

8abfec5c5d868f…e8630b2db1b0af

2 in → 1 out24.7000 XPM274 B

AZAGtx3d…zGQTU9Z1

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.

2.530 × 10¹⁰³(104-digit number)

25303363808340327636…02303925608509963021

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

2.530 × 10¹⁰³(104-digit number)

25303363808340327636…02303925608509963021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.060 × 10¹⁰³(104-digit number)

50606727616680655272…04607851217019926041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.012 × 10¹⁰⁴(105-digit number)

10121345523336131054…09215702434039852081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.024 × 10¹⁰⁴(105-digit number)

20242691046672262108…18431404868079704161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.048 × 10¹⁰⁴(105-digit number)

40485382093344524217…36862809736159408321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.097 × 10¹⁰⁴(105-digit number)

80970764186689048435…73725619472318816641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.619 × 10¹⁰⁵(106-digit number)

16194152837337809687…47451238944637633281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.238 × 10¹⁰⁵(106-digit number)

32388305674675619374…94902477889275266561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.477 × 10¹⁰⁵(106-digit number)

64776611349351238748…89804955778550533121

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