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Block #2,637,205

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 8:39:57 PM Β· Difficulty 11.4269 Β· 4,194,519 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
378579e1e59240f7c32042712f87178a094ac17ef5042fa965bfa9334580351e
View on Chainz β†—

Height

#2,637,205

Difficulty

11.426920

Transactions

2

Size

425 B

Version

2

Bits

0b6d4a9c

Nonce

69,651,236

Timestamp

4/29/2018, 8:39:57 PM

Confirmations

4,194,519

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

b622760b32a772edbd785c58f13317c352da3cdd10802a1d8b344062d9fdc7a5
Transactions (2)
Coinbasee10ce19b67cb9d…69bb9d3950804f
1 in β†’ 1 out7.6600 XPM110 B
Adqah8zh…1WwoHJ9t
9279c118cd3d6f…1bef7f52df365d
1 in β†’ 2 out163488.0782 XPM226 B
AcNRsf8r…rFKsfhSHAGafMD9U…qUye8cWT
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.

3.126 Γ— 10⁹³(94-digit number)
31261956658686344378…30998889776594474649
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.126 Γ— 10⁹³(94-digit number)
31261956658686344378…30998889776594474649
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.252 Γ— 10⁹³(94-digit number)
62523913317372688757…61997779553188949299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁴(95-digit number)
12504782663474537751…23995559106377898599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.500 Γ— 10⁹⁴(95-digit number)
25009565326949075502…47991118212755797199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.001 Γ— 10⁹⁴(95-digit number)
50019130653898151005…95982236425511594399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁡(96-digit number)
10003826130779630201…91964472851023188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.000 Γ— 10⁹⁡(96-digit number)
20007652261559260402…83928945702046377599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.001 Γ— 10⁹⁡(96-digit number)
40015304523118520804…67857891404092755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.003 Γ— 10⁹⁡(96-digit number)
80030609046237041609…35715782808185510399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁢(97-digit number)
16006121809247408321…71431565616371020799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.201 Γ— 10⁹⁢(97-digit number)
32012243618494816643…42863131232742041599
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,897,897 XPMΒ·at block #6,831,723 Β· updates every 60s
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