Block #599,994

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/24/2014, 1:54:43 AM · Difficulty 10.9253 · 6,225,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
31377a52656bcef995d373de438be3ec37a43baae876435d44b507269a1c9238

Height

#599,994

Difficulty

10.925269

Transactions

2

Size

434 B

Version

2

Bits

0aecde70

Nonce

764,576,426

Timestamp

6/24/2014, 1:54:43 AM

Confirmations

6,225,316

Merkle Root

d6717804b9ddca72f1cd2489fa3a309a7079bbcfb734af38211a7ca0d0ce5a1f
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.

3.090 × 10⁹⁸(99-digit number)
30909058545101230625…41759930988568868001
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
3.090 × 10⁹⁸(99-digit number)
30909058545101230625…41759930988568868001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.181 × 10⁹⁸(99-digit number)
61818117090202461250…83519861977137736001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.236 × 10⁹⁹(100-digit number)
12363623418040492250…67039723954275472001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.472 × 10⁹⁹(100-digit number)
24727246836080984500…34079447908550944001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.945 × 10⁹⁹(100-digit number)
49454493672161969000…68158895817101888001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.890 × 10⁹⁹(100-digit number)
98908987344323938001…36317791634203776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.978 × 10¹⁰⁰(101-digit number)
19781797468864787600…72635583268407552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.956 × 10¹⁰⁰(101-digit number)
39563594937729575200…45271166536815104001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.912 × 10¹⁰⁰(101-digit number)
79127189875459150400…90542333073630208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.582 × 10¹⁰¹(102-digit number)
15825437975091830080…81084666147260416001
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:57,846,583 XPM·at block #6,825,309 · updates every 60s
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