Block #28,094

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 11:05:18 AM · Difficulty 7.9809 · 6,784,696 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4523d79fd22836ca4338014c4b8ace264e170dbd0e326009e317f6b1e8bec5b2

Height

#28,094

Difficulty

7.980911

Transactions

1

Size

199 B

Version

2

Bits

07fb1d01

Nonce

188

Timestamp

7/13/2013, 11:05:18 AM

Confirmations

6,784,696

Merkle Root

eb17861f07693215c96718a430b62e699a8565a15111460b23d5798d4bc262dd
Transactions (1)
1 in → 1 out15.6800 XPM109 B
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.

1.407 × 10⁹⁵(96-digit number)
14070609791233658079…48533571444054426011
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
1.407 × 10⁹⁵(96-digit number)
14070609791233658079…48533571444054426011
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.814 × 10⁹⁵(96-digit number)
28141219582467316158…97067142888108852021
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.628 × 10⁹⁵(96-digit number)
56282439164934632317…94134285776217704041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.125 × 10⁹⁶(97-digit number)
11256487832986926463…88268571552435408081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.251 × 10⁹⁶(97-digit number)
22512975665973852926…76537143104870816161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.502 × 10⁹⁶(97-digit number)
45025951331947705853…53074286209741632321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.005 × 10⁹⁶(97-digit number)
90051902663895411707…06148572419483264641
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,746,362 XPM·at block #6,812,789 · updates every 60s
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