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Block #2,542,071

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/28/2018, 6:47:06 AM Β· Difficulty 10.9874 Β· 4,289,628 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2c6f4666e333178c20bb37d94558c7063bf5f53c9c683498f74310c0505630cc
View on Chainz β†—

Height

#2,542,071

Difficulty

10.987417

Transactions

2

Size

573 B

Version

2

Bits

0afcc75b

Nonce

1,141,224,771

Timestamp

2/28/2018, 6:47:06 AM

Confirmations

4,289,628

Mined by

⛏️ P2SHASw4DnL1uK42WSiigruAA1MyMh17j7beoB

Merkle Root

adee12d45a65e865f2c066d0baff27d06df45c7eb140fef87a1b88cde971fdd1
Transactions (2)
Coinbasef565a477a80e9f…735d9f90a6c06b
1 in β†’ 1 out8.2800 XPM110 B
ASw4DnL1…17j7beoB
e52ce45ac2a0f9…12a7b89a4e88a6
2 in β†’ 2 out506.5567 XPM374 B
AP76z3HF…9BRXjC7tAGGn6SJu…QVxKbSrU
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.

1.611 Γ— 10⁹²(93-digit number)
16110559778444060738…66696505324520787201
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
1.611 Γ— 10⁹²(93-digit number)
16110559778444060738…66696505324520787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.222 Γ— 10⁹²(93-digit number)
32221119556888121476…33393010649041574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.444 Γ— 10⁹²(93-digit number)
64442239113776242952…66786021298083148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.288 Γ— 10⁹³(94-digit number)
12888447822755248590…33572042596166297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.577 Γ— 10⁹³(94-digit number)
25776895645510497180…67144085192332595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.155 Γ— 10⁹³(94-digit number)
51553791291020994361…34288170384665190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.031 Γ— 10⁹⁴(95-digit number)
10310758258204198872…68576340769330380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.062 Γ— 10⁹⁴(95-digit number)
20621516516408397744…37152681538660761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.124 Γ— 10⁹⁴(95-digit number)
41243033032816795489…74305363077321523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.248 Γ— 10⁹⁴(95-digit number)
82486066065633590978…48610726154643046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.649 Γ— 10⁹⁡(96-digit number)
16497213213126718195…97221452309286092801
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:57,897,701 XPMΒ·at block #6,831,698 Β· updates every 60s
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