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Block #2,651,481

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2018, 8:43:46 PM Β· Difficulty 11.7509 Β· 4,185,153 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9f3c63443677e2b9de1382118fbea487983ea1dc660baf7f51a5c613ccdfe7a
View on Chainz β†—

Height

#2,651,481

Difficulty

11.750912

Transactions

2

Size

724 B

Version

2

Bits

0bc03bbf

Nonce

73,767,140

Timestamp

5/6/2018, 8:43:46 PM

Confirmations

4,185,153

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

9c2d6713f5b79394da5e6ce398507fb9e98c04737fee73a29f940362119c6a45
Transactions (2)
Coinbase92a58b7a15bf10…9266b0995db839
1 in β†’ 1 out7.2400 XPM110 B
Adqah8zh…1WwoHJ9t
46b9c1bc566a33…670a8a939c12f6
3 in β†’ 2 out4.2232 XPM524 B
AVpmQyvd…cc7QQQhxAZBKJEgo…Kr8zAAQn
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.

3.168 Γ— 10⁹⁴(95-digit number)
31685438702241681485…26997614243266974801
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
3.168 Γ— 10⁹⁴(95-digit number)
31685438702241681485…26997614243266974801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.337 Γ— 10⁹⁴(95-digit number)
63370877404483362971…53995228486533949601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.267 Γ— 10⁹⁡(96-digit number)
12674175480896672594…07990456973067899201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.534 Γ— 10⁹⁡(96-digit number)
25348350961793345188…15980913946135798401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.069 Γ— 10⁹⁡(96-digit number)
50696701923586690376…31961827892271596801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10139340384717338075…63923655784543193601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20278680769434676150…27847311569086387201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.055 Γ— 10⁹⁢(97-digit number)
40557361538869352301…55694623138172774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.111 Γ— 10⁹⁢(97-digit number)
81114723077738704602…11389246276345548801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.622 Γ— 10⁹⁷(98-digit number)
16222944615547740920…22778492552691097601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.244 Γ— 10⁹⁷(98-digit number)
32445889231095481841…45556985105382195201
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:57,937,344 XPMΒ·at block #6,836,633 Β· updates every 60s
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