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Block #2,163,543

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2017, 7:41:41 PM Β· Difficulty 10.8999 Β· 4,662,892 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
411634ba747d8e1b99a2ee74f741d648089cbd410efc9648b69389a338377ecf
View on Chainz β†—

Height

#2,163,543

Difficulty

10.899881

Transactions

2

Size

2.84 KB

Version

2

Bits

0ae65e98

Nonce

989,747,791

Timestamp

6/16/2017, 7:41:41 PM

Confirmations

4,662,892

Mined by

⛏️ P2SHAG9tZw9nEyuAwZPLpxrhEHk8Cg6wXFx8Be

Merkle Root

c58efc8829b2ed46ad46271c21ea20fd0cbe6ad01c0d65afd78c34e390714570
Transactions (2)
Coinbase15928322075031…851c942cd05afb
1 in β†’ 1 out8.4800 XPM109 B
AG9tZw9n…6wXFx8Be
ec2f1e5f0f207a…07bcd9117c27be
18 in β†’ 1 out312.3373 XPM2.64 KB
AYAuRWxY…Rg3t4M63
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.

2.680 Γ— 10⁹⁴(95-digit number)
26807941319019691744…93909559601675916801
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
2.680 Γ— 10⁹⁴(95-digit number)
26807941319019691744…93909559601675916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.361 Γ— 10⁹⁴(95-digit number)
53615882638039383488…87819119203351833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.072 Γ— 10⁹⁡(96-digit number)
10723176527607876697…75638238406703667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.144 Γ— 10⁹⁡(96-digit number)
21446353055215753395…51276476813407334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.289 Γ— 10⁹⁡(96-digit number)
42892706110431506790…02552953626814668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.578 Γ— 10⁹⁡(96-digit number)
85785412220863013581…05105907253629337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.715 Γ— 10⁹⁢(97-digit number)
17157082444172602716…10211814507258675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.431 Γ— 10⁹⁢(97-digit number)
34314164888345205432…20423629014517350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.862 Γ— 10⁹⁢(97-digit number)
68628329776690410865…40847258029034700801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.372 Γ— 10⁹⁷(98-digit number)
13725665955338082173…81694516058069401601
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:57,855,617 XPMΒ·at block #6,826,434 Β· updates every 60s
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