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Block #2,762,365

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/24/2018, 1:08:41 AM Β· Difficulty 11.6548 Β· 4,081,316 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
43640b54a1d0652ab65bfe1bf38f64accb2376b14f69f9d2c7b1719a76823d7a
View on Chainz β†—

Height

#2,762,365

Difficulty

11.654787

Transactions

1

Size

200 B

Version

2

Bits

0ba7a026

Nonce

474,147,129

Timestamp

7/24/2018, 1:08:41 AM

Confirmations

4,081,316

Mined by

⛏️ P2SHAcFnKMX639MnZKZAZvYBKR3yENDP3p3sq2

Merkle Root

33a663d70e7947ef46868b2503b14e49bf67ee5dfa2280667b369a26973b4655
Transactions (1)
Coinbase33a663d70e7947…369a26973b4655
1 in β†’ 1 out7.3500 XPM110 B
AcFnKMX6…DP3p3sq2
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.

1.634 Γ— 10⁹⁴(95-digit number)
16348483058075151845…92005623640334502559
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
1.634 Γ— 10⁹⁴(95-digit number)
16348483058075151845…92005623640334502559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.269 Γ— 10⁹⁴(95-digit number)
32696966116150303691…84011247280669005119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.539 Γ— 10⁹⁴(95-digit number)
65393932232300607382…68022494561338010239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.307 Γ— 10⁹⁡(96-digit number)
13078786446460121476…36044989122676020479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.615 Γ— 10⁹⁡(96-digit number)
26157572892920242952…72089978245352040959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.231 Γ— 10⁹⁡(96-digit number)
52315145785840485905…44179956490704081919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁢(97-digit number)
10463029157168097181…88359912981408163839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁢(97-digit number)
20926058314336194362…76719825962816327679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.185 Γ— 10⁹⁢(97-digit number)
41852116628672388724…53439651925632655359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.370 Γ— 10⁹⁢(97-digit number)
83704233257344777449…06879303851265310719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁷(98-digit number)
16740846651468955489…13758607702530621439
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:57,993,821 XPMΒ·at block #6,843,680 Β· updates every 60s
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