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Block #2,795,866

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2018, 1:02:23 AM Β· Difficulty 11.6815 Β· 4,041,112 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d493b5adb4bdaf9cbe0bbb2f35898ce835f0edd4d3c8c0fc78f5b421a7e85f36
View on Chainz β†—

Height

#2,795,866

Difficulty

11.681522

Transactions

1

Size

201 B

Version

2

Bits

0bae783c

Nonce

8,703,379

Timestamp

8/16/2018, 1:02:23 AM

Confirmations

4,041,112

Mined by

⛏️ P2SHANBgyoMx9JxzTauM9UhXzCpro7RiFRvje9

Merkle Root

4ffad97135da89b62d9388fcb769b80d089fc93066285066b3b9ee114227f406
Transactions (1)
Coinbase4ffad97135da89…b9ee114227f406
1 in β†’ 1 out7.3200 XPM110 B
ANBgyoMx…RiFRvje9
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.

5.204 Γ— 10⁹⁢(97-digit number)
52045949344632957692…92043442409504194561
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
5.204 Γ— 10⁹⁢(97-digit number)
52045949344632957692…92043442409504194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.040 Γ— 10⁹⁷(98-digit number)
10409189868926591538…84086884819008389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.081 Γ— 10⁹⁷(98-digit number)
20818379737853183077…68173769638016778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.163 Γ— 10⁹⁷(98-digit number)
41636759475706366154…36347539276033556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.327 Γ— 10⁹⁷(98-digit number)
83273518951412732308…72695078552067112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.665 Γ— 10⁹⁸(99-digit number)
16654703790282546461…45390157104134225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.330 Γ— 10⁹⁸(99-digit number)
33309407580565092923…90780314208268451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.661 Γ— 10⁹⁸(99-digit number)
66618815161130185846…81560628416536903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.332 Γ— 10⁹⁹(100-digit number)
13323763032226037169…63121256833073807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.664 Γ— 10⁹⁹(100-digit number)
26647526064452074338…26242513666147614721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.329 Γ— 10⁹⁹(100-digit number)
53295052128904148677…52485027332295229441
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:57,940,123 XPMΒ·at block #6,836,977 Β· updates every 60s
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