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Block #3,045,766

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/9/2019, 4:08:35 PM Β· Difficulty 10.9961 Β· 3,796,416 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e7887ba053691c1e173812ece3a5e5fbd59af40ff04c6301069fe5292d5cd340
View on Chainz β†—

Height

#3,045,766

Difficulty

10.996091

Transactions

1

Size

201 B

Version

2

Bits

0afeffce

Nonce

34,295,287

Timestamp

2/9/2019, 4:08:35 PM

Confirmations

3,796,416

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

d527599e8cf93bf6eb1fb09533d237e7dd3d5c43b6ac0fc74c09fea30a7b2e42
Transactions (1)
Coinbased527599e8cf93b…09fea30a7b2e42
1 in β†’ 1 out8.2600 XPM110 B
AUhjokok…k5m93PZR
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.

1.190 Γ— 10⁹⁷(98-digit number)
11905481512485103897…89800435440064481279
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
1.190 Γ— 10⁹⁷(98-digit number)
11905481512485103897…89800435440064481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.381 Γ— 10⁹⁷(98-digit number)
23810963024970207794…79600870880128962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.762 Γ— 10⁹⁷(98-digit number)
47621926049940415589…59201741760257925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.524 Γ— 10⁹⁷(98-digit number)
95243852099880831178…18403483520515850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.904 Γ— 10⁹⁸(99-digit number)
19048770419976166235…36806967041031700479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.809 Γ— 10⁹⁸(99-digit number)
38097540839952332471…73613934082063400959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.619 Γ— 10⁹⁸(99-digit number)
76195081679904664943…47227868164126801919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁹(100-digit number)
15239016335980932988…94455736328253603839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.047 Γ— 10⁹⁹(100-digit number)
30478032671961865977…88911472656507207679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.095 Γ— 10⁹⁹(100-digit number)
60956065343923731954…77822945313014415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.219 Γ— 10¹⁰⁰(101-digit number)
12191213068784746390…55645890626028830719
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:57,981,848 XPMΒ·at block #6,842,181 Β· updates every 60s
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