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Block #2,096,555

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2017, 1:52:04 AM Β· Difficulty 10.8724 Β· 4,744,868 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
77415391a6a169d337311f9759487b618d74a931f5627a15593111bdf7b6cafb
View on Chainz β†—

Height

#2,096,555

Difficulty

10.872365

Transactions

1

Size

200 B

Version

2

Bits

0adf534d

Nonce

501,940,700

Timestamp

5/2/2017, 1:52:04 AM

Confirmations

4,744,868

Mined by

⛏️ P2SHAbQozoZDDuhbZGen12TXcCYaDxJH1VdiAv

Merkle Root

dda462205cf6f883d73a45b87e25faf2272f4cf4ed7ac5a20e778aaebd397b57
Transactions (1)
Coinbasedda462205cf6f8…778aaebd397b57
1 in β†’ 1 out8.4500 XPM109 B
AbQozoZD…JH1VdiAv
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.

5.002 Γ— 10⁹⁢(97-digit number)
50022653716988983286…68328156354956421121
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
5.002 Γ— 10⁹⁢(97-digit number)
50022653716988983286…68328156354956421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.000 Γ— 10⁹⁷(98-digit number)
10004530743397796657…36656312709912842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.000 Γ— 10⁹⁷(98-digit number)
20009061486795593314…73312625419825684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.001 Γ— 10⁹⁷(98-digit number)
40018122973591186629…46625250839651368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.003 Γ— 10⁹⁷(98-digit number)
80036245947182373258…93250501679302737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.600 Γ— 10⁹⁸(99-digit number)
16007249189436474651…86501003358605475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.201 Γ— 10⁹⁸(99-digit number)
32014498378872949303…73002006717210951681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.402 Γ— 10⁹⁸(99-digit number)
64028996757745898606…46004013434421903361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.280 Γ— 10⁹⁹(100-digit number)
12805799351549179721…92008026868843806721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.561 Γ— 10⁹⁹(100-digit number)
25611598703098359442…84016053737687613441
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:57,975,760 XPMΒ·at block #6,841,422 Β· updates every 60s
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