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Block #3,048,698

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/11/2019, 6:15:16 PM Β· Difficulty 10.9961 Β· 3,791,638 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e4e0b4109bb2a34795bbdbe1b3d80e86b4db03b7837f66ab1d13dac3b6e66543
View on Chainz β†—

Height

#3,048,698

Difficulty

10.996091

Transactions

2

Size

869 B

Version

2

Bits

0afeffd8

Nonce

212,027,741

Timestamp

2/11/2019, 6:15:16 PM

Confirmations

3,791,638

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

cd85ae81d7de4e2c0e42650b40f3aa031fb7b7f5a4a89c7d8a303e6bed4736e1
Transactions (2)
Coinbase3441cd7e97e506…68e5487912ea46
1 in β†’ 1 out8.2700 XPM110 B
AUhjokok…k5m93PZR
7722815e4de1a4…da9bcc0b8b3f6b
4 in β†’ 2 out304.9043 XPM668 B
AdYmwPx5…q86kyBPeARo9Bx54…mTopc3JB
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.

6.334 Γ— 10⁹⁷(98-digit number)
63341518436698542012…18025934562929976319
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
6.334 Γ— 10⁹⁷(98-digit number)
63341518436698542012…18025934562929976319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.266 Γ— 10⁹⁸(99-digit number)
12668303687339708402…36051869125859952639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.533 Γ— 10⁹⁸(99-digit number)
25336607374679416805…72103738251719905279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.067 Γ— 10⁹⁸(99-digit number)
50673214749358833610…44207476503439810559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.013 Γ— 10⁹⁹(100-digit number)
10134642949871766722…88414953006879621119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.026 Γ— 10⁹⁹(100-digit number)
20269285899743533444…76829906013759242239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.053 Γ— 10⁹⁹(100-digit number)
40538571799487066888…53659812027518484479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.107 Γ— 10⁹⁹(100-digit number)
81077143598974133776…07319624055036968959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.621 Γ— 10¹⁰⁰(101-digit number)
16215428719794826755…14639248110073937919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.243 Γ— 10¹⁰⁰(101-digit number)
32430857439589653510…29278496220147875839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.486 Γ— 10¹⁰⁰(101-digit number)
64861714879179307021…58556992440295751679
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:57,967,009 XPMΒ·at block #6,840,335 Β· updates every 60s
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