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Block #2,173,373

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/23/2017, 7:05:46 AM Β· Difficulty 10.9097 Β· 4,660,340 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ae6a560e8f08e05f9e063281c052eca07067783d49334b487c4698153d38f622
View on Chainz β†—

Height

#2,173,373

Difficulty

10.909712

Transactions

1

Size

200 B

Version

2

Bits

0ae8e2e1

Nonce

399,588,311

Timestamp

6/23/2017, 7:05:46 AM

Confirmations

4,660,340

Mined by

⛏️ P2SHAKSJg1nHZDiNobSqUuRvfm8geqGWLo3hRn

Merkle Root

5e0cd267761d92ee7b08c38f1831b75943a733ce338a616e53bf75020c12a323
Transactions (1)
Coinbase5e0cd267761d92…bf75020c12a323
1 in β†’ 1 out8.3900 XPM109 B
AKSJg1nH…GWLo3hRn
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.

1.787 Γ— 10⁹⁢(97-digit number)
17877053313410161852…31597331631844410881
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
1.787 Γ— 10⁹⁢(97-digit number)
17877053313410161852…31597331631844410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.575 Γ— 10⁹⁢(97-digit number)
35754106626820323704…63194663263688821761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.150 Γ— 10⁹⁢(97-digit number)
71508213253640647409…26389326527377643521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.430 Γ— 10⁹⁷(98-digit number)
14301642650728129481…52778653054755287041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.860 Γ— 10⁹⁷(98-digit number)
28603285301456258963…05557306109510574081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.720 Γ— 10⁹⁷(98-digit number)
57206570602912517927…11114612219021148161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.144 Γ— 10⁹⁸(99-digit number)
11441314120582503585…22229224438042296321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.288 Γ— 10⁹⁸(99-digit number)
22882628241165007171…44458448876084592641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.576 Γ— 10⁹⁸(99-digit number)
45765256482330014342…88916897752169185281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.153 Γ— 10⁹⁸(99-digit number)
91530512964660028684…77833795504338370561
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:57,913,926 XPMΒ·at block #6,833,712 Β· updates every 60s
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