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Block #2,636,320

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 1:11:56 PM Β· Difficulty 11.3749 Β· 4,207,268 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2ec2e7fe7dc7c86723b0e3ad107d2612026a1a2687b21b2638057951afc692f
View on Chainz β†—

Height

#2,636,320

Difficulty

11.374894

Transactions

2

Size

13.13 KB

Version

2

Bits

0b5ff90e

Nonce

357,741,629

Timestamp

4/29/2018, 1:11:56 PM

Confirmations

4,207,268

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

4ca3cc4fefce465c6448ce010930d0dbbf3c4b30d8ddd7d274c82f8c8380f5bc
Transactions (2)
Coinbase43d1decd451178…e7af96b509f445
1 in β†’ 1 out7.8600 XPM110 B
Adqah8zh…1WwoHJ9t
a9923a52bbe8cc…2d742eec649530
115 in β†’ 2 out1035.0569 XPM12.93 KB
ANLd1Ear…UpXZNRL2AQeup8Da…8drhocze
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.

2.188 Γ— 10⁹⁴(95-digit number)
21880490927839644014…53508789797188375381
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
2.188 Γ— 10⁹⁴(95-digit number)
21880490927839644014…53508789797188375381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.376 Γ— 10⁹⁴(95-digit number)
43760981855679288028…07017579594376750761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.752 Γ— 10⁹⁴(95-digit number)
87521963711358576057…14035159188753501521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.750 Γ— 10⁹⁡(96-digit number)
17504392742271715211…28070318377507003041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.500 Γ— 10⁹⁡(96-digit number)
35008785484543430423…56140636755014006081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.001 Γ— 10⁹⁡(96-digit number)
70017570969086860846…12281273510028012161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.400 Γ— 10⁹⁢(97-digit number)
14003514193817372169…24562547020056024321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.800 Γ— 10⁹⁢(97-digit number)
28007028387634744338…49125094040112048641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.601 Γ— 10⁹⁢(97-digit number)
56014056775269488676…98250188080224097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.120 Γ— 10⁹⁷(98-digit number)
11202811355053897735…96500376160448194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.240 Γ— 10⁹⁷(98-digit number)
22405622710107795470…93000752320896389121
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:57,993,064 XPMΒ·at block #6,843,587 Β· updates every 60s
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