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Block #265,452

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 2:01:41 PM Β· Difficulty 9.9626 Β· 6,551,526 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a8a12897a5a8d0b776f2debcac51bcfd8500c248a01a8b66a4e3971183d8560
View on Chainz β†—

Height

#265,452

Difficulty

9.962619

Transactions

1

Size

206 B

Version

2

Bits

09f66e3a

Nonce

33,554,903

Timestamp

11/19/2013, 2:01:41 PM

Confirmations

6,551,526

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

648f650a011f67d62d6f25c897f1d24b0f282027631bf57529ef06596c04a330
Transactions (1)
Coinbase648f650a011f67…ef06596c04a330
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.231 Γ— 10⁹⁡(96-digit number)
82311511602875586159…64242277487103657201
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
8.231 Γ— 10⁹⁡(96-digit number)
82311511602875586159…64242277487103657201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.646 Γ— 10⁹⁢(97-digit number)
16462302320575117231…28484554974207314401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.292 Γ— 10⁹⁢(97-digit number)
32924604641150234463…56969109948414628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.584 Γ— 10⁹⁢(97-digit number)
65849209282300468927…13938219896829257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.316 Γ— 10⁹⁷(98-digit number)
13169841856460093785…27876439793658515201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.633 Γ— 10⁹⁷(98-digit number)
26339683712920187571…55752879587317030401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.267 Γ— 10⁹⁷(98-digit number)
52679367425840375142…11505759174634060801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.053 Γ— 10⁹⁸(99-digit number)
10535873485168075028…23011518349268121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.107 Γ— 10⁹⁸(99-digit number)
21071746970336150056…46023036698536243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.214 Γ— 10⁹⁸(99-digit number)
42143493940672300113…92046073397072486401
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:57,779,862 XPMΒ·at block #6,816,977 Β· updates every 60s
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