XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,823,096

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/3/2018, 4:49:57 PM Β· Difficulty 11.7044 Β· 4,013,592 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ad4506a6d1484052aff8e11ac876718ae7581a9c8eae4d61dd38897a437eb83
View on Chainz β†—

Height

#2,823,096

Difficulty

11.704395

Transactions

1

Size

200 B

Version

2

Bits

0bb45335

Nonce

1,279,070,839

Timestamp

9/3/2018, 4:49:57 PM

Confirmations

4,013,592

Mined by

⛏️ P2SHAUR3dvA27dd6t9B3N2bX11EBqchQHBuPqs

Merkle Root

0fde5afe5ddfc34d4a586ab20cf6ede6460904190280b34a53c95e29cd9eb79a
Transactions (1)
Coinbase0fde5afe5ddfc3…c95e29cd9eb79a
1 in β†’ 1 out7.2900 XPM110 B
AUR3dvA2…hQHBuPqs
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.

3.006 Γ— 10⁹⁴(95-digit number)
30064520785579158662…28125571651483939839
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
3.006 Γ— 10⁹⁴(95-digit number)
30064520785579158662…28125571651483939839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.012 Γ— 10⁹⁴(95-digit number)
60129041571158317324…56251143302967879679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.202 Γ— 10⁹⁡(96-digit number)
12025808314231663464…12502286605935759359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.405 Γ— 10⁹⁡(96-digit number)
24051616628463326929…25004573211871518719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.810 Γ— 10⁹⁡(96-digit number)
48103233256926653859…50009146423743037439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.620 Γ— 10⁹⁡(96-digit number)
96206466513853307719…00018292847486074879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.924 Γ— 10⁹⁢(97-digit number)
19241293302770661543…00036585694972149759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.848 Γ— 10⁹⁢(97-digit number)
38482586605541323087…00073171389944299519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.696 Γ— 10⁹⁢(97-digit number)
76965173211082646175…00146342779888599039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.539 Γ— 10⁹⁷(98-digit number)
15393034642216529235…00292685559777198079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.078 Γ— 10⁹⁷(98-digit number)
30786069284433058470…00585371119554396159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
6.157 Γ— 10⁹⁷(98-digit number)
61572138568866116940…01170742239108792319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,937,786 XPMΒ·at block #6,836,687 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