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Block #2,655,696

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2018, 9:46:10 AM Β· Difficulty 11.7031 Β· 4,187,561 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a44645400a3c2318ffb610aafb797ff06a8cfe67b5af75df21b60f45fabec3f1
View on Chainz β†—

Height

#2,655,696

Difficulty

11.703068

Transactions

1

Size

198 B

Version

2

Bits

0bb3fc4a

Nonce

1,489,440,041

Timestamp

5/10/2018, 9:46:10 AM

Confirmations

4,187,561

Mined by

⛏️ P2SHAV851rdsmFGiZiq8jYxYL651HD54HqfNQM

Merkle Root

b8be142dd2800133c44731c9ad4ee5f245036316a415eb90705672ca0f60847b
Transactions (1)
Coinbaseb8be142dd28001…5672ca0f60847b
1 in β†’ 1 out7.2900 XPM109 B
AV851rds…54HqfNQM
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.

3.013 Γ— 10⁹²(93-digit number)
30130121913031147029…88842810131391817721
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
3.013 Γ— 10⁹²(93-digit number)
30130121913031147029…88842810131391817721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.026 Γ— 10⁹²(93-digit number)
60260243826062294059…77685620262783635441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.205 Γ— 10⁹³(94-digit number)
12052048765212458811…55371240525567270881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.410 Γ— 10⁹³(94-digit number)
24104097530424917623…10742481051134541761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.820 Γ— 10⁹³(94-digit number)
48208195060849835247…21484962102269083521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.641 Γ— 10⁹³(94-digit number)
96416390121699670495…42969924204538167041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.928 Γ— 10⁹⁴(95-digit number)
19283278024339934099…85939848409076334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.856 Γ— 10⁹⁴(95-digit number)
38566556048679868198…71879696818152668161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.713 Γ— 10⁹⁴(95-digit number)
77133112097359736396…43759393636305336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.542 Γ— 10⁹⁡(96-digit number)
15426622419471947279…87518787272610672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.085 Γ— 10⁹⁡(96-digit number)
30853244838943894558…75037574545221345281
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:57,990,428 XPMΒ·at block #6,843,256 Β· updates every 60s
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