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Block #326,260

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/23/2013, 4:09:14 PM Β· Difficulty 10.1927 Β· 6,481,626 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
021e40e44fa9b0f12986844df809d38bcbb9b5798c05b407fb8da63e280931c8
View on Chainz β†—

Height

#326,260

Difficulty

10.192713

Transactions

1

Size

204 B

Version

2

Bits

0a3155a5

Nonce

47,777

Timestamp

12/23/2013, 4:09:14 PM

Confirmations

6,481,626

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6ab9c07a42ead7deca876fdece8c5dbbf44d6aba5d32508d2a44b5a978907748
Transactions (1)
Coinbase6ab9c07a42ead7…44b5a978907748
1 in β†’ 1 out9.6100 XPM116 B
AbwWkWZt…kawDhufa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.230 Γ— 10⁸⁹(90-digit number)
12305059267534694265…52178981531973644551
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.230 Γ— 10⁸⁹(90-digit number)
12305059267534694265…52178981531973644551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.461 Γ— 10⁸⁹(90-digit number)
24610118535069388531…04357963063947289101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.922 Γ— 10⁸⁹(90-digit number)
49220237070138777063…08715926127894578201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.844 Γ— 10⁸⁹(90-digit number)
98440474140277554127…17431852255789156401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.968 Γ— 10⁹⁰(91-digit number)
19688094828055510825…34863704511578312801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.937 Γ— 10⁹⁰(91-digit number)
39376189656111021650…69727409023156625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.875 Γ— 10⁹⁰(91-digit number)
78752379312222043301…39454818046313251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.575 Γ— 10⁹¹(92-digit number)
15750475862444408660…78909636092626502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.150 Γ— 10⁹¹(92-digit number)
31500951724888817320…57819272185253004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.300 Γ— 10⁹¹(92-digit number)
63001903449777634641…15638544370506009601
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,707,123 XPMΒ·at block #6,807,885 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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