Block #326,200

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/23/2013, 3:01:41 PM · Difficulty 10.1939 · 6,490,020 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e6dceff720650fcf26b98c1f2ed21a15de468263dcb640f221dde9ba52508b24

Height

#326,200

Difficulty

10.193915

Transactions

2

Size

394 B

Version

2

Bits

0a31a46c

Nonce

61,249

Timestamp

12/23/2013, 3:01:41 PM

Confirmations

6,490,020

Merkle Root

5236185bd5bd28884e1dc7b9936222e0846786379009cb20ad0d4db41c399aaf
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.

1.433 × 10⁹⁹(100-digit number)
14338644949204669043…20136201673492044801
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
1.433 × 10⁹⁹(100-digit number)
14338644949204669043…20136201673492044801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.867 × 10⁹⁹(100-digit number)
28677289898409338086…40272403346984089601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.735 × 10⁹⁹(100-digit number)
57354579796818676172…80544806693968179201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.147 × 10¹⁰⁰(101-digit number)
11470915959363735234…61089613387936358401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.294 × 10¹⁰⁰(101-digit number)
22941831918727470468…22179226775872716801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.588 × 10¹⁰⁰(101-digit number)
45883663837454940937…44358453551745433601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.176 × 10¹⁰⁰(101-digit number)
91767327674909881875…88716907103490867201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.835 × 10¹⁰¹(102-digit number)
18353465534981976375…77433814206981734401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.670 × 10¹⁰¹(102-digit number)
36706931069963952750…54867628413963468801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.341 × 10¹⁰¹(102-digit number)
73413862139927905500…09735256827926937601
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:57,773,889 XPM·at block #6,816,219 · updates every 60s
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