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Block #2,831,905

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2018, 3:35:55 PM Β· Difficulty 11.7187 Β· 4,012,602 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc55bf81ed26acafc63cd72aada19638a9f117a07331c93cd40ca0449be63984
View on Chainz β†—

Height

#2,831,905

Difficulty

11.718669

Transactions

1

Size

200 B

Version

2

Bits

0bb7fab5

Nonce

115,097,536

Timestamp

9/9/2018, 3:35:55 PM

Confirmations

4,012,602

Mined by

⛏️ P2SHAbSX4L9ud5yG4Xa2ntEJpmPqrXeSiKH2Zg

Merkle Root

1d3b3e08f0abc7d72415f7b5640edb5285ca31aed339e941f7719f9534d52b57
Transactions (1)
Coinbase1d3b3e08f0abc7…719f9534d52b57
1 in β†’ 1 out7.2700 XPM109 B
AbSX4L9u…eSiKH2Zg
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.

1.082 Γ— 10⁹⁢(97-digit number)
10827667039601323009…60227367346270003201
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
1.082 Γ— 10⁹⁢(97-digit number)
10827667039601323009…60227367346270003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.165 Γ— 10⁹⁢(97-digit number)
21655334079202646018…20454734692540006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.331 Γ— 10⁹⁢(97-digit number)
43310668158405292036…40909469385080012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.662 Γ— 10⁹⁢(97-digit number)
86621336316810584072…81818938770160025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.732 Γ— 10⁹⁷(98-digit number)
17324267263362116814…63637877540320051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.464 Γ— 10⁹⁷(98-digit number)
34648534526724233629…27275755080640102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.929 Γ— 10⁹⁷(98-digit number)
69297069053448467258…54551510161280204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.385 Γ— 10⁹⁸(99-digit number)
13859413810689693451…09103020322560409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.771 Γ— 10⁹⁸(99-digit number)
27718827621379386903…18206040645120819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.543 Γ— 10⁹⁸(99-digit number)
55437655242758773806…36412081290241638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.108 Γ— 10⁹⁹(100-digit number)
11087531048551754761…72824162580483276801
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:58,000,454 XPMΒ·at block #6,844,506 Β· updates every 60s
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