Block #67,094

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/19/2013, 8:56:24 PM · Difficulty 8.9874 · 6,723,900 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d0fa61c30b15ee74d9999d1c3221e18d6707b241a7afaa67f116fe0fa85a17a

Height

#67,094

Difficulty

8.987374

Transactions

2

Size

656 B

Version

2

Bits

08fcc483

Nonce

470

Timestamp

7/19/2013, 8:56:24 PM

Confirmations

6,723,900

Merkle Root

388435eefa0199246c5cfeb376a0c7ff26c5c6c469734fe4cb8593406b93a5f2
Transactions (2)
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.

1.325 × 10¹⁰⁰(101-digit number)
13257617365460386870…30908891550199519071
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.

1
origin + 1
1.325 × 10¹⁰⁰(101-digit number)
13257617365460386870…30908891550199519071
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.651 × 10¹⁰⁰(101-digit number)
26515234730920773741…61817783100399038141
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.303 × 10¹⁰⁰(101-digit number)
53030469461841547483…23635566200798076281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.060 × 10¹⁰¹(102-digit number)
10606093892368309496…47271132401596152561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.121 × 10¹⁰¹(102-digit number)
21212187784736618993…94542264803192305121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.242 × 10¹⁰¹(102-digit number)
42424375569473237986…89084529606384610241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.484 × 10¹⁰¹(102-digit number)
84848751138946475973…78169059212769220481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.696 × 10¹⁰²(103-digit number)
16969750227789295194…56338118425538440961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.393 × 10¹⁰²(103-digit number)
33939500455578590389…12676236851076881921
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, …
Circulating Supply:57,571,966 XPM·at block #6,790,993 · updates every 60s