XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,051,393

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/13/2019, 5:05:41 PM Β· Difficulty 10.9961 Β· 3,792,596 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
461bd2e3345ce4de166b24a706d6a62e9b6fb6c2e85a2b2d9e42697aa6abaada
View on Chainz β†—

Height

#3,051,393

Difficulty

10.996085

Transactions

2

Size

721 B

Version

2

Bits

0afeff70

Nonce

416,614,685

Timestamp

2/13/2019, 5:05:41 PM

Confirmations

3,792,596

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

34397dcc6cb7a7f5093cf14e8a9cd5dff530fe59477465bbcd007c4cee2193d5
Transactions (2)
Coinbaseb5db27f4edede0…04b4558ea4f66a
1 in β†’ 1 out8.2700 XPM109 B
AUhjokok…k5m93PZR
6f30a0dbcb524c…3a19bcd02a6cda
3 in β†’ 2 out31.0325 XPM522 B
AeTHTL7A…vT1872bkAbun3buW…K5HLBBBE
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.

4.150 Γ— 10⁹⁡(96-digit number)
41506244982970094322…82675598398100367359
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
4.150 Γ— 10⁹⁡(96-digit number)
41506244982970094322…82675598398100367359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.301 Γ— 10⁹⁡(96-digit number)
83012489965940188645…65351196796200734719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁢(97-digit number)
16602497993188037729…30702393592401469439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.320 Γ— 10⁹⁢(97-digit number)
33204995986376075458…61404787184802938879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.640 Γ— 10⁹⁢(97-digit number)
66409991972752150916…22809574369605877759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.328 Γ— 10⁹⁷(98-digit number)
13281998394550430183…45619148739211755519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.656 Γ— 10⁹⁷(98-digit number)
26563996789100860366…91238297478423511039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.312 Γ— 10⁹⁷(98-digit number)
53127993578201720732…82476594956847022079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁸(99-digit number)
10625598715640344146…64953189913694044159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.125 Γ— 10⁹⁸(99-digit number)
21251197431280688293…29906379827388088319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.250 Γ— 10⁹⁸(99-digit number)
42502394862561376586…59812759654776176639
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:57,996,292 XPMΒ·at block #6,843,988 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy