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Block #2,643,401

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 2:27:38 AM Β· Difficulty 11.6820 Β· 4,195,609 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
680ecd38a940360e3f44db987afeb64ff38117b3856a09bb39e830b71af844e1
View on Chainz β†—

Height

#2,643,401

Difficulty

11.682044

Transactions

1

Size

200 B

Version

2

Bits

0bae9a6f

Nonce

195,455,767

Timestamp

5/2/2018, 2:27:38 AM

Confirmations

4,195,609

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

447d1825f910c647638e287f7f740c4063496a74b517feb72cde49753a8a70a3
Transactions (1)
Coinbase447d1825f910c6…de49753a8a70a3
1 in β†’ 1 out7.3200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

8.653 Γ— 10⁹³(94-digit number)
86533190482848863066…45422817594282229761
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
8.653 Γ— 10⁹³(94-digit number)
86533190482848863066…45422817594282229761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.730 Γ— 10⁹⁴(95-digit number)
17306638096569772613…90845635188564459521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.461 Γ— 10⁹⁴(95-digit number)
34613276193139545226…81691270377128919041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.922 Γ— 10⁹⁴(95-digit number)
69226552386279090453…63382540754257838081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.384 Γ— 10⁹⁡(96-digit number)
13845310477255818090…26765081508515676161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.769 Γ— 10⁹⁡(96-digit number)
27690620954511636181…53530163017031352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.538 Γ— 10⁹⁡(96-digit number)
55381241909023272362…07060326034062704641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.107 Γ— 10⁹⁢(97-digit number)
11076248381804654472…14120652068125409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.215 Γ— 10⁹⁢(97-digit number)
22152496763609308945…28241304136250818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.430 Γ— 10⁹⁢(97-digit number)
44304993527218617890…56482608272501637121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.860 Γ— 10⁹⁢(97-digit number)
88609987054437235780…12965216545003274241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,956,347 XPMΒ·at block #6,839,009 Β· updates every 60s
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