XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,806,029

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/23/2018, 5:19:17 AM Β· Difficulty 11.6706 Β· 4,037,499 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
92516247eceb12675bf51c28a6d5e86bded7d8855ad9d277f588654ea0a0ba84
View on Chainz β†—

Height

#2,806,029

Difficulty

11.670622

Transactions

1

Size

200 B

Version

2

Bits

0babade5

Nonce

567,155,202

Timestamp

8/23/2018, 5:19:17 AM

Confirmations

4,037,499

Mined by

⛏️ P2SHAYdG69Hbeh8gLHkC4cyUbWZEHuqvRkMbyD

Merkle Root

3a19967156a9f3a1c7f302bd19dfc317ccc141b10cd8ddf1318ee3b4151edad9
Transactions (1)
Coinbase3a19967156a9f3…8ee3b4151edad9
1 in β†’ 1 out7.3300 XPM110 B
AYdG69Hb…qvRkMbyD
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.

4.737 Γ— 10⁹⁴(95-digit number)
47375657633002103587…13756227701479251359
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
4.737 Γ— 10⁹⁴(95-digit number)
47375657633002103587…13756227701479251359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.475 Γ— 10⁹⁴(95-digit number)
94751315266004207174…27512455402958502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.895 Γ— 10⁹⁡(96-digit number)
18950263053200841434…55024910805917005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.790 Γ— 10⁹⁡(96-digit number)
37900526106401682869…10049821611834010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.580 Γ— 10⁹⁡(96-digit number)
75801052212803365739…20099643223668021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.516 Γ— 10⁹⁢(97-digit number)
15160210442560673147…40199286447336043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.032 Γ— 10⁹⁢(97-digit number)
30320420885121346295…80398572894672087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.064 Γ— 10⁹⁢(97-digit number)
60640841770242692591…60797145789344174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁷(98-digit number)
12128168354048538518…21594291578688348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.425 Γ— 10⁹⁷(98-digit number)
24256336708097077036…43188583157376696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.851 Γ— 10⁹⁷(98-digit number)
48512673416194154073…86377166314753392639
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:57,992,601 XPMΒ·at block #6,843,527 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