Block #592,896

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/18/2014, 6:26:58 AM · Difficulty 10.9417 · 6,223,262 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
769aa6bf0a66e1a4f2349ab7fe80ef67750b246a0b2ccfb68609dd981d1e3268

Height

#592,896

Difficulty

10.941689

Transactions

5

Size

2.21 KB

Version

2

Bits

0af11284

Nonce

129,110,888

Timestamp

6/18/2014, 6:26:58 AM

Confirmations

6,223,262

Merkle Root

e9429a3362682d8e416303a220cbd3211ca65ca17c9d2dbc8b52c1ff4e206df8
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.

2.380 × 10⁹⁷(98-digit number)
23800022324419570081…38507181723303772401
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
2.380 × 10⁹⁷(98-digit number)
23800022324419570081…38507181723303772401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.760 × 10⁹⁷(98-digit number)
47600044648839140162…77014363446607544801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.520 × 10⁹⁷(98-digit number)
95200089297678280325…54028726893215089601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.904 × 10⁹⁸(99-digit number)
19040017859535656065…08057453786430179201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.808 × 10⁹⁸(99-digit number)
38080035719071312130…16114907572860358401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.616 × 10⁹⁸(99-digit number)
76160071438142624260…32229815145720716801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.523 × 10⁹⁹(100-digit number)
15232014287628524852…64459630291441433601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.046 × 10⁹⁹(100-digit number)
30464028575257049704…28919260582882867201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.092 × 10⁹⁹(100-digit number)
60928057150514099408…57838521165765734401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.218 × 10¹⁰⁰(101-digit number)
12185611430102819881…15677042331531468801
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, …
Circulating Supply:57,773,386 XPM·at block #6,816,157 · updates every 60s
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