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Block #1,371,819

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2015, 6:40:11 PM Β· Difficulty 10.8103 Β· 5,469,303 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f7587cd0e6f7bd0c5830682c39c8be041af0ddde22e7af13cf748b9e86671d4b
View on Chainz β†—

Height

#1,371,819

Difficulty

10.810260

Transactions

1

Size

200 B

Version

2

Bits

0acf6d3b

Nonce

1,511,819,068

Timestamp

12/16/2015, 6:40:11 PM

Confirmations

5,469,303

Mined by

⛏️ P2SHATgx1J93kaKUyC8Ti4if37RRmLaUynXZSd

Merkle Root

80ca8c669377b5b9e490bf68d675645849e27cfbed12b7baaba658932b4f5ba5
Transactions (1)
Coinbase80ca8c669377b5…a658932b4f5ba5
1 in β†’ 1 out8.5400 XPM110 B
ATgx1J93…aUynXZSd
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.

1.264 Γ— 10⁹⁴(95-digit number)
12646988471284496538…78396361063880520641
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
1.264 Γ— 10⁹⁴(95-digit number)
12646988471284496538…78396361063880520641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.529 Γ— 10⁹⁴(95-digit number)
25293976942568993077…56792722127761041281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.058 Γ— 10⁹⁴(95-digit number)
50587953885137986155…13585444255522082561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.011 Γ— 10⁹⁡(96-digit number)
10117590777027597231…27170888511044165121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.023 Γ— 10⁹⁡(96-digit number)
20235181554055194462…54341777022088330241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.047 Γ— 10⁹⁡(96-digit number)
40470363108110388924…08683554044176660481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.094 Γ— 10⁹⁡(96-digit number)
80940726216220777848…17367108088353320961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.618 Γ— 10⁹⁢(97-digit number)
16188145243244155569…34734216176706641921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.237 Γ— 10⁹⁢(97-digit number)
32376290486488311139…69468432353413283841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.475 Γ— 10⁹⁢(97-digit number)
64752580972976622279…38936864706826567681
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:57,973,345 XPMΒ·at block #6,841,121 Β· updates every 60s
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