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Block #346,143

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/6/2014, 9:27:56 AM Β· Difficulty 10.2182 Β· 6,461,311 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fe3148eb215a8a39adcdc69b05844e8f51427cc98fad707eaa35c671fde10ae
View on Chainz β†—

Height

#346,143

Difficulty

10.218215

Transactions

1

Size

206 B

Version

2

Bits

0a37dcea

Nonce

59,001

Timestamp

1/6/2014, 9:27:56 AM

Confirmations

6,461,311

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7c1fe9a43886e7f1ced0544e13e18178300e1611a8bc9016cee522531eace294
Transactions (1)
Coinbase7c1fe9a43886e7…e522531eace294
1 in β†’ 1 out9.5600 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.

8.368 Γ— 10⁹⁡(96-digit number)
83684349164262235983…10568275477761304801
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
8.368 Γ— 10⁹⁡(96-digit number)
83684349164262235983…10568275477761304801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.673 Γ— 10⁹⁢(97-digit number)
16736869832852447196…21136550955522609601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.347 Γ— 10⁹⁢(97-digit number)
33473739665704894393…42273101911045219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.694 Γ— 10⁹⁢(97-digit number)
66947479331409788786…84546203822090438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13389495866281957757…69092407644180876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.677 Γ— 10⁹⁷(98-digit number)
26778991732563915514…38184815288361753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.355 Γ— 10⁹⁷(98-digit number)
53557983465127831029…76369630576723507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.071 Γ— 10⁹⁸(99-digit number)
10711596693025566205…52739261153447014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.142 Γ— 10⁹⁸(99-digit number)
21423193386051132411…05478522306894028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.284 Γ— 10⁹⁸(99-digit number)
42846386772102264823…10957044613788057601
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:57,703,655 XPMΒ·at block #6,807,453 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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