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Block #2,680,526

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/27/2018, 6:41:56 PM Β· Difficulty 11.6927 Β· 4,156,417 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
80cf98936ea26098054adeab544345cc3f5d5e337138dac60e9afce3330cc27a
View on Chainz β†—

Height

#2,680,526

Difficulty

11.692731

Transactions

2

Size

869 B

Version

2

Bits

0bb156d8

Nonce

821,902,712

Timestamp

5/27/2018, 6:41:56 PM

Confirmations

4,156,417

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8532c46bb3c75cf43b8855916a484a98c14c94a0ccf0e00307cf9fa21b7e4aae
Transactions (2)
Coinbase0816169e2ebc45…b99b42d64c7338
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
1d5c1fb47b0e91…23fa5918a28335
4 in β†’ 2 out404.9687 XPM668 B
AcAp95Kg…7crDd9jqAKf74TEF…iNryuktP
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.

1.938 Γ— 10⁹⁷(98-digit number)
19387308327015826504…12559713391960217599
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
1.938 Γ— 10⁹⁷(98-digit number)
19387308327015826504…12559713391960217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.877 Γ— 10⁹⁷(98-digit number)
38774616654031653008…25119426783920435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.754 Γ— 10⁹⁷(98-digit number)
77549233308063306016…50238853567840870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.550 Γ— 10⁹⁸(99-digit number)
15509846661612661203…00477707135681740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.101 Γ— 10⁹⁸(99-digit number)
31019693323225322406…00955414271363481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.203 Γ— 10⁹⁸(99-digit number)
62039386646450644813…01910828542726963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁹(100-digit number)
12407877329290128962…03821657085453926399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.481 Γ— 10⁹⁹(100-digit number)
24815754658580257925…07643314170907852799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.963 Γ— 10⁹⁹(100-digit number)
49631509317160515850…15286628341815705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.926 Γ— 10⁹⁹(100-digit number)
99263018634321031701…30573256683631411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.985 Γ— 10¹⁰⁰(101-digit number)
19852603726864206340…61146513367262822399
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:57,939,842 XPMΒ·at block #6,836,942 Β· updates every 60s
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