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Block #2,295,926

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2017, 12:15:41 PM Β· Difficulty 10.9511 Β· 4,546,171 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19efc9b619f63626d96516c4238b4157d0a5151e8d65d46ff07273c688a24969
View on Chainz β†—

Height

#2,295,926

Difficulty

10.951089

Transactions

1

Size

200 B

Version

2

Bits

0af37a92

Nonce

1,853,486,046

Timestamp

9/14/2017, 12:15:41 PM

Confirmations

4,546,171

Mined by

⛏️ P2SHASxxUZLKGGwLFu1ysC28xf3n9EEMjHXH62

Merkle Root

84886d725adbba52d52192e6926453ec98bb30446d1454c4adf7374a11f4c0ea
Transactions (1)
Coinbase84886d725adbba…f7374a11f4c0ea
1 in β†’ 1 out8.3300 XPM110 B
ASxxUZLK…EMjHXH62
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.

1.760 Γ— 10⁹⁴(95-digit number)
17607150885182514151…44667189119938473161
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
1.760 Γ— 10⁹⁴(95-digit number)
17607150885182514151…44667189119938473161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.521 Γ— 10⁹⁴(95-digit number)
35214301770365028302…89334378239876946321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.042 Γ— 10⁹⁴(95-digit number)
70428603540730056605…78668756479753892641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.408 Γ— 10⁹⁡(96-digit number)
14085720708146011321…57337512959507785281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.817 Γ— 10⁹⁡(96-digit number)
28171441416292022642…14675025919015570561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.634 Γ— 10⁹⁡(96-digit number)
56342882832584045284…29350051838031141121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.126 Γ— 10⁹⁢(97-digit number)
11268576566516809056…58700103676062282241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.253 Γ— 10⁹⁢(97-digit number)
22537153133033618113…17400207352124564481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.507 Γ— 10⁹⁢(97-digit number)
45074306266067236227…34800414704249128961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.014 Γ— 10⁹⁢(97-digit number)
90148612532134472455…69600829408498257921
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:57,981,162 XPMΒ·at block #6,842,096 Β· updates every 60s
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