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Block #332,704

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/28/2013, 6:24:12 AM Β· Difficulty 10.1665 Β· 6,493,731 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
105a79834609a53f3efff76728668b89dca68580fa0cdb63f7a90c131f5aabd8
View on Chainz β†—

Height

#332,704

Difficulty

10.166477

Transactions

1

Size

200 B

Version

2

Bits

0a2a9e3d

Nonce

76,752

Timestamp

12/28/2013, 6:24:12 AM

Confirmations

6,493,731

Mined by

⛏️ P2SHAeifvHEVbnQDYLQnrNi1oaThM63Gg34VUW

Merkle Root

e6aa5e12586805c88bde7891834be963a79ece628b790f77dbbff47afa34de4e
Transactions (1)
Coinbasee6aa5e12586805…bff47afa34de4e
1 in β†’ 1 out9.6600 XPM109 B
AeifvHEV…3Gg34VUW
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.

4.541 Γ— 10⁹⁷(98-digit number)
45418112075289293798…47465047161538072581
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
4.541 Γ— 10⁹⁷(98-digit number)
45418112075289293798…47465047161538072581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.083 Γ— 10⁹⁷(98-digit number)
90836224150578587597…94930094323076145161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.816 Γ— 10⁹⁸(99-digit number)
18167244830115717519…89860188646152290321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.633 Γ— 10⁹⁸(99-digit number)
36334489660231435038…79720377292304580641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.266 Γ— 10⁹⁸(99-digit number)
72668979320462870077…59440754584609161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.453 Γ— 10⁹⁹(100-digit number)
14533795864092574015…18881509169218322561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.906 Γ— 10⁹⁹(100-digit number)
29067591728185148031…37763018338436645121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.813 Γ— 10⁹⁹(100-digit number)
58135183456370296062…75526036676873290241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.162 Γ— 10¹⁰⁰(101-digit number)
11627036691274059212…51052073353746580481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.325 Γ— 10¹⁰⁰(101-digit number)
23254073382548118424…02104146707493160961
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:57,855,617 XPMΒ·at block #6,826,434 Β· updates every 60s
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