Block #592,266

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/17/2014, 6:02:00 PM · Difficulty 10.9430 · 6,203,071 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
29d8032b89ba114b5f7405d967499cac7f052f8c2f164f75e302f1d1bf6c82b2

Height

#592,266

Difficulty

10.942957

Transactions

4

Size

1.59 KB

Version

2

Bits

0af1659a

Nonce

1,999,836,809

Timestamp

6/17/2014, 6:02:00 PM

Confirmations

6,203,071

Merkle Root

648c661e00959aead0c72df6dfb222e7b614967116b7ea54dd32bd04f09ae377
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.

2.379 × 10⁹⁹(100-digit number)
23795504247717617358…79453273394139955201
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
2.379 × 10⁹⁹(100-digit number)
23795504247717617358…79453273394139955201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.759 × 10⁹⁹(100-digit number)
47591008495435234717…58906546788279910401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.518 × 10⁹⁹(100-digit number)
95182016990870469435…17813093576559820801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.903 × 10¹⁰⁰(101-digit number)
19036403398174093887…35626187153119641601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.807 × 10¹⁰⁰(101-digit number)
38072806796348187774…71252374306239283201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.614 × 10¹⁰⁰(101-digit number)
76145613592696375548…42504748612478566401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.522 × 10¹⁰¹(102-digit number)
15229122718539275109…85009497224957132801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.045 × 10¹⁰¹(102-digit number)
30458245437078550219…70018994449914265601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.091 × 10¹⁰¹(102-digit number)
60916490874157100438…40037988899828531201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.218 × 10¹⁰²(103-digit number)
12183298174831420087…80075977799657062401
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:57,606,755 XPM·at block #6,795,336 · updates every 60s
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