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Block #2,100,499

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2017, 6:06:12 AM Β· Difficulty 10.8555 Β· 4,741,166 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c5d3039a8da4a4de47cc883e8d46a0e0a6340ff20dc98bd7192a1a1f5cd99f60
View on Chainz β†—

Height

#2,100,499

Difficulty

10.855504

Transactions

1

Size

199 B

Version

2

Bits

0adb0249

Nonce

442,880,425

Timestamp

5/5/2017, 6:06:12 AM

Confirmations

4,741,166

Mined by

⛏️ P2SHAP5e3CZBkQLXvUvF542W8nAvSQmnqYtvfr

Merkle Root

b265c01433e88a91b74ee2e72987d0dc7c9e0d128209830b62a214d31cddfe26
Transactions (1)
Coinbaseb265c01433e88a…a214d31cddfe26
1 in β†’ 1 out8.4700 XPM109 B
AP5e3CZB…mnqYtvfr
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.

6.235 Γ— 10⁹³(94-digit number)
62359250880623175558…21121465159381393441
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
6.235 Γ— 10⁹³(94-digit number)
62359250880623175558…21121465159381393441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.247 Γ— 10⁹⁴(95-digit number)
12471850176124635111…42242930318762786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.494 Γ— 10⁹⁴(95-digit number)
24943700352249270223…84485860637525573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.988 Γ— 10⁹⁴(95-digit number)
49887400704498540446…68971721275051147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.977 Γ— 10⁹⁴(95-digit number)
99774801408997080892…37943442550102295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.995 Γ— 10⁹⁡(96-digit number)
19954960281799416178…75886885100204590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.990 Γ— 10⁹⁡(96-digit number)
39909920563598832357…51773770200409180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.981 Γ— 10⁹⁡(96-digit number)
79819841127197664714…03547540400818360321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15963968225439532942…07095080801636720641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.192 Γ— 10⁹⁢(97-digit number)
31927936450879065885…14190161603273441281
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:57,977,709 XPMΒ·at block #6,841,664 Β· updates every 60s
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