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Block #2,100,444

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2017, 5:25:06 AM Β· Difficulty 10.8551 Β· 4,744,115 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b649eca7d7635b88e40d9c3d9b4192f75229855303cb31119a6a1d423994ebc
View on Chainz β†—

Height

#2,100,444

Difficulty

10.855118

Transactions

1

Size

200 B

Version

2

Bits

0adae8ff

Nonce

1,951,633,032

Timestamp

5/5/2017, 5:25:06 AM

Confirmations

4,744,115

Mined by

⛏️ P2SHAa5PFdYANQskZ1CYjxvz3Zwvi79ECJ9uL5

Merkle Root

535bb5ad5e515c3e94c53fd02f8d07e4b080035e34d3c1379e1ba2c9cd58860e
Transactions (1)
Coinbase535bb5ad5e515c…1ba2c9cd58860e
1 in β†’ 1 out8.4700 XPM110 B
Aa5PFdYA…9ECJ9uL5
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.

3.616 Γ— 10⁹³(94-digit number)
36160912908677669083…65287720910117161131
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
3.616 Γ— 10⁹³(94-digit number)
36160912908677669083…65287720910117161131
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.232 Γ— 10⁹³(94-digit number)
72321825817355338167…30575441820234322261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.446 Γ— 10⁹⁴(95-digit number)
14464365163471067633…61150883640468644521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.892 Γ— 10⁹⁴(95-digit number)
28928730326942135267…22301767280937289041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.785 Γ— 10⁹⁴(95-digit number)
57857460653884270534…44603534561874578081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.157 Γ— 10⁹⁡(96-digit number)
11571492130776854106…89207069123749156161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.314 Γ— 10⁹⁡(96-digit number)
23142984261553708213…78414138247498312321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.628 Γ— 10⁹⁡(96-digit number)
46285968523107416427…56828276494996624641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.257 Γ— 10⁹⁡(96-digit number)
92571937046214832854…13656552989993249281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.851 Γ— 10⁹⁢(97-digit number)
18514387409242966570…27313105979986498561
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:58,000,874 XPMΒ·at block #6,844,558 Β· updates every 60s
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