Block #483,599

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 3:34:42 AM · Difficulty 10.5660 · 6,332,998 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f3fbe13aa1374daebd29c8da5c33d0fa9226401e614e0e41a20d4f4ecbd32a93

Height

#483,599

Difficulty

10.566039

Transactions

11

Size

2.56 KB

Version

2

Bits

0a90e7f6

Nonce

199,064,331

Timestamp

4/10/2014, 3:34:42 AM

Confirmations

6,332,998

Merkle Root

429af04b4b7a86b0adc0e5579cf0d8b376c6c64eed717d1dd5bd57fcf34eb397
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.

2.320 × 10⁹⁹(100-digit number)
23205599113144911100…84255117936238320641
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
2.320 × 10⁹⁹(100-digit number)
23205599113144911100…84255117936238320641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.641 × 10⁹⁹(100-digit number)
46411198226289822200…68510235872476641281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.282 × 10⁹⁹(100-digit number)
92822396452579644400…37020471744953282561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.856 × 10¹⁰⁰(101-digit number)
18564479290515928880…74040943489906565121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.712 × 10¹⁰⁰(101-digit number)
37128958581031857760…48081886979813130241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.425 × 10¹⁰⁰(101-digit number)
74257917162063715520…96163773959626260481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.485 × 10¹⁰¹(102-digit number)
14851583432412743104…92327547919252520961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.970 × 10¹⁰¹(102-digit number)
29703166864825486208…84655095838505041921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.940 × 10¹⁰¹(102-digit number)
59406333729650972416…69310191677010083841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.188 × 10¹⁰²(103-digit number)
11881266745930194483…38620383354020167681
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:57,776,901 XPM·at block #6,816,596 · updates every 60s
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