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Block #2,873,779

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/9/2018, 8:32:01 AM Β· Difficulty 11.6651 Β· 3,971,051 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca40593bc065ccb1b2fbfcc9dd7131cc57a8865de12c78f84474e0317b2d0af0
View on Chainz β†—

Height

#2,873,779

Difficulty

11.665082

Transactions

1

Size

200 B

Version

2

Bits

0baa42d3

Nonce

505,364,544

Timestamp

10/9/2018, 8:32:01 AM

Confirmations

3,971,051

Mined by

⛏️ P2SHAGdLMCnas89YduEwZF6JeyMoGzeSwH6AdN

Merkle Root

d19eaa89a46410a148a13738be8ff418a4a79dd9926988d3392d5e5fecdf8565
Transactions (1)
Coinbased19eaa89a46410…2d5e5fecdf8565
1 in β†’ 1 out7.3400 XPM110 B
AGdLMCna…eSwH6AdN
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.

1.353 Γ— 10⁹⁡(96-digit number)
13537447215848154116…14850393540770758259
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
1.353 Γ— 10⁹⁡(96-digit number)
13537447215848154116…14850393540770758259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.707 Γ— 10⁹⁡(96-digit number)
27074894431696308232…29700787081541516519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.414 Γ— 10⁹⁡(96-digit number)
54149788863392616464…59401574163083033039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁢(97-digit number)
10829957772678523292…18803148326166066079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.165 Γ— 10⁹⁢(97-digit number)
21659915545357046585…37606296652332132159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.331 Γ— 10⁹⁢(97-digit number)
43319831090714093171…75212593304664264319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.663 Γ— 10⁹⁢(97-digit number)
86639662181428186343…50425186609328528639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.732 Γ— 10⁹⁷(98-digit number)
17327932436285637268…00850373218657057279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.465 Γ— 10⁹⁷(98-digit number)
34655864872571274537…01700746437314114559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.931 Γ— 10⁹⁷(98-digit number)
69311729745142549074…03401492874628229119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁸(99-digit number)
13862345949028509814…06802985749256458239
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:58,003,049 XPMΒ·at block #6,844,829 Β· updates every 60s
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