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Block #2,122,391

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 2:24:38 PM Β· Difficulty 10.9155 Β· 4,720,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f66ca6d599877d5add00d4288693762cbf2fc5b6bc63162931fc6b08a431dbc8
View on Chainz β†—

Height

#2,122,391

Difficulty

10.915544

Transactions

1

Size

200 B

Version

2

Bits

0aea611f

Nonce

475,705,843

Timestamp

5/18/2017, 2:24:38 PM

Confirmations

4,720,656

Mined by

⛏️ P2SHAHWHuEHM3F2gs6P34C75kYMB5Nw315AbKp

Merkle Root

f1a7d693fe7c84497dd2c45fff3844f336576142b46de97f5b93c1faa34e7134
Transactions (1)
Coinbasef1a7d693fe7c84…93c1faa34e7134
1 in β†’ 1 out8.3800 XPM110 B
AHWHuEHM…w315AbKp
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.

5.828 Γ— 10⁹⁴(95-digit number)
58284035020173463206…46081307361055156601
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
5.828 Γ— 10⁹⁴(95-digit number)
58284035020173463206…46081307361055156601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.165 Γ— 10⁹⁡(96-digit number)
11656807004034692641…92162614722110313201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.331 Γ— 10⁹⁡(96-digit number)
23313614008069385282…84325229444220626401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.662 Γ— 10⁹⁡(96-digit number)
46627228016138770565…68650458888441252801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.325 Γ— 10⁹⁡(96-digit number)
93254456032277541130…37300917776882505601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.865 Γ— 10⁹⁢(97-digit number)
18650891206455508226…74601835553765011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.730 Γ— 10⁹⁢(97-digit number)
37301782412911016452…49203671107530022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.460 Γ— 10⁹⁢(97-digit number)
74603564825822032904…98407342215060044801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.492 Γ— 10⁹⁷(98-digit number)
14920712965164406580…96814684430120089601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.984 Γ— 10⁹⁷(98-digit number)
29841425930328813161…93629368860240179201
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:57,988,733 XPMΒ·at block #6,843,046 Β· updates every 60s
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