Block #2,479,066

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2018, 4:44:42 PM · Difficulty 10.9658 · 4,365,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
49535a741997087e27592f104351249214b5d9ea3dc622a0ff6f66c49e5c8345

Height

#2,479,066

Difficulty

10.965818

Transactions

3

Size

1.26 KB

Version

2

Bits

0af73fde

Nonce

1,906,482,496

Timestamp

1/18/2018, 4:44:42 PM

Confirmations

4,365,850

Merkle Root

247f95d00379ab5578fda56c88ef9a8f5123d5c00e18236b30b0db6cc7e0134d
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.

1.003 × 10⁹⁷(98-digit number)
10039139470961864558…27600921767586908161
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
1.003 × 10⁹⁷(98-digit number)
10039139470961864558…27600921767586908161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.007 × 10⁹⁷(98-digit number)
20078278941923729116…55201843535173816321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.015 × 10⁹⁷(98-digit number)
40156557883847458232…10403687070347632641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.031 × 10⁹⁷(98-digit number)
80313115767694916464…20807374140695265281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.606 × 10⁹⁸(99-digit number)
16062623153538983292…41614748281390530561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.212 × 10⁹⁸(99-digit number)
32125246307077966585…83229496562781061121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.425 × 10⁹⁸(99-digit number)
64250492614155933171…66458993125562122241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.285 × 10⁹⁹(100-digit number)
12850098522831186634…32917986251124244481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.570 × 10⁹⁹(100-digit number)
25700197045662373268…65835972502248488961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.140 × 10⁹⁹(100-digit number)
51400394091324746537…31671945004496977921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.028 × 10¹⁰⁰(101-digit number)
10280078818264949307…63343890008993955841
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,003,744 XPM·at block #6,844,915 · updates every 60s
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