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Block #2,162,368

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/15/2017, 11:10:17 PM Β· Difficulty 10.9010 Β· 4,673,976 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
033445ac7d48991571b4d871ffd820d78634c89da1d75fdaed760fa6ab29c77e
View on Chainz β†—

Height

#2,162,368

Difficulty

10.900964

Transactions

2

Size

1.57 KB

Version

2

Bits

0ae6a593

Nonce

767,151,495

Timestamp

6/15/2017, 11:10:17 PM

Confirmations

4,673,976

Mined by

⛏️ P2SHAW7SrK1vzsrEwhQ8G2FtJ2jC4kk3XpS6xv

Merkle Root

a7c2e78cf104971b54accc2cffaab8c37efba4f226471929b3cb27347e6fa748
Transactions (2)
Coinbasee448c77898c9e7…c74e66501f2b0e
1 in β†’ 1 out8.5000 XPM109 B
AW7SrK1v…k3XpS6xv
27748703a0906d…e543c00f5173e1
9 in β†’ 2 out6487.8100 XPM1.38 KB
ALjVzEH6…ZtoUaFFiAd99QL7a…dPAkBCCh
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.

2.389 Γ— 10⁹²(93-digit number)
23892946181690596440…46399779287103417671
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
2.389 Γ— 10⁹²(93-digit number)
23892946181690596440…46399779287103417671
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.778 Γ— 10⁹²(93-digit number)
47785892363381192881…92799558574206835341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.557 Γ— 10⁹²(93-digit number)
95571784726762385763…85599117148413670681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.911 Γ— 10⁹³(94-digit number)
19114356945352477152…71198234296827341361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.822 Γ— 10⁹³(94-digit number)
38228713890704954305…42396468593654682721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.645 Γ— 10⁹³(94-digit number)
76457427781409908611…84792937187309365441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.529 Γ— 10⁹⁴(95-digit number)
15291485556281981722…69585874374618730881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.058 Γ— 10⁹⁴(95-digit number)
30582971112563963444…39171748749237461761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.116 Γ— 10⁹⁴(95-digit number)
61165942225127926888…78343497498474923521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.223 Γ— 10⁹⁡(96-digit number)
12233188445025585377…56686994996949847041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.446 Γ— 10⁹⁡(96-digit number)
24466376890051170755…13373989993899694081
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:57,935,010 XPMΒ·at block #6,836,343 Β· updates every 60s
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