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Block #373,290

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/24/2014, 5:13:24 AM Β· Difficulty 10.4254 Β· 6,437,184 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
84ca538756c241e146404b13511d060023fee86393c821ccc7bb20185fc9aeee
View on Chainz β†—

Height

#373,290

Difficulty

10.425447

Transactions

1

Size

201 B

Version

2

Bits

0a6cea12

Nonce

209,299

Timestamp

1/24/2014, 5:13:24 AM

Confirmations

6,437,184

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7e8ca731d55fba9d3c9eb97616b9bd8bb10e59211dccae9af644390b7740e728
Transactions (1)
Coinbase7e8ca731d55fba…44390b7740e728
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

6.901 Γ— 10⁹⁢(97-digit number)
69015608494752235807…55923868608381907621
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
6.901 Γ— 10⁹⁢(97-digit number)
69015608494752235807…55923868608381907621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.380 Γ— 10⁹⁷(98-digit number)
13803121698950447161…11847737216763815241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.760 Γ— 10⁹⁷(98-digit number)
27606243397900894323…23695474433527630481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.521 Γ— 10⁹⁷(98-digit number)
55212486795801788646…47390948867055260961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.104 Γ— 10⁹⁸(99-digit number)
11042497359160357729…94781897734110521921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.208 Γ— 10⁹⁸(99-digit number)
22084994718320715458…89563795468221043841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.416 Γ— 10⁹⁸(99-digit number)
44169989436641430916…79127590936442087681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.833 Γ— 10⁹⁸(99-digit number)
88339978873282861833…58255181872884175361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.766 Γ— 10⁹⁹(100-digit number)
17667995774656572366…16510363745768350721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.533 Γ— 10⁹⁹(100-digit number)
35335991549313144733…33020727491536701441
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:57,727,871 XPMΒ·at block #6,810,473 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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