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Block #2,661,925

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2018, 10:33:00 AM Β· Difficulty 11.6370 Β· 4,177,022 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9cb04022d2a6e44dd6beebdc524fbb22d7086fa5541d2fc2775f6f20e9e3043d
View on Chainz β†—

Height

#2,661,925

Difficulty

11.636972

Transactions

2

Size

871 B

Version

2

Bits

0ba31092

Nonce

1,310,376,006

Timestamp

5/15/2018, 10:33:00 AM

Confirmations

4,177,022

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e27f590856338ce9379d7edead75fa1df495666a83221db0f6fbf45927a651a2
Transactions (2)
Coinbaseb96fa23121376c…31d1f80a030509
1 in β†’ 1 out7.3800 XPM109 B
Adqah8zh…1WwoHJ9t
f6af7008372266…f820cf21e02f86
4 in β†’ 2 out9937.8700 XPM671 B
ANfHnS6i…cmJ5JwZUALssV9Qd…PvJB43wd
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.

5.945 Γ— 10⁹⁡(96-digit number)
59453303569978131699…45886838282388368321
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
5.945 Γ— 10⁹⁡(96-digit number)
59453303569978131699…45886838282388368321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.189 Γ— 10⁹⁢(97-digit number)
11890660713995626339…91773676564776736641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.378 Γ— 10⁹⁢(97-digit number)
23781321427991252679…83547353129553473281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.756 Γ— 10⁹⁢(97-digit number)
47562642855982505359…67094706259106946561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.512 Γ— 10⁹⁢(97-digit number)
95125285711965010719…34189412518213893121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.902 Γ— 10⁹⁷(98-digit number)
19025057142393002143…68378825036427786241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.805 Γ— 10⁹⁷(98-digit number)
38050114284786004287…36757650072855572481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.610 Γ— 10⁹⁷(98-digit number)
76100228569572008575…73515300145711144961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.522 Γ— 10⁹⁸(99-digit number)
15220045713914401715…47030600291422289921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.044 Γ— 10⁹⁸(99-digit number)
30440091427828803430…94061200582844579841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.088 Γ— 10⁹⁸(99-digit number)
60880182855657606860…88122401165689159681
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:57,955,842 XPMΒ·at block #6,838,946 Β· updates every 60s
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