XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,876,132

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/11/2018, 1:48:42 AM Β· Difficulty 11.6570 Β· 3,966,050 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
203b7268d91e67ba52eb0d8cc99e067cb086edec3bc2c35221aec8b81bde282f
View on Chainz β†—

Height

#2,876,132

Difficulty

11.656966

Transactions

1

Size

200 B

Version

2

Bits

0ba82ef4

Nonce

1,180,293,432

Timestamp

10/11/2018, 1:48:42 AM

Confirmations

3,966,050

Mined by

⛏️ P2SHASuyhf4W3tnSYQY4dudUGkdqmVacDbRv8e

Merkle Root

fb48d13ed02c7dacc050d1e567211828d62123921c86d47409afbafd18e8f979
Transactions (1)
Coinbasefb48d13ed02c7d…afbafd18e8f979
1 in β†’ 1 out7.3500 XPM110 B
ASuyhf4W…acDbRv8e
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.

1.717 Γ— 10⁹⁡(96-digit number)
17172893802979753172…78104186554244157399
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
1.717 Γ— 10⁹⁡(96-digit number)
17172893802979753172…78104186554244157399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.434 Γ— 10⁹⁡(96-digit number)
34345787605959506344…56208373108488314799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.869 Γ— 10⁹⁡(96-digit number)
68691575211919012689…12416746216976629599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.373 Γ— 10⁹⁢(97-digit number)
13738315042383802537…24833492433953259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.747 Γ— 10⁹⁢(97-digit number)
27476630084767605075…49666984867906518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.495 Γ— 10⁹⁢(97-digit number)
54953260169535210151…99333969735813036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.099 Γ— 10⁹⁷(98-digit number)
10990652033907042030…98667939471626073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.198 Γ— 10⁹⁷(98-digit number)
21981304067814084060…97335878943252147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.396 Γ— 10⁹⁷(98-digit number)
43962608135628168121…94671757886504294399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.792 Γ— 10⁹⁷(98-digit number)
87925216271256336242…89343515773008588799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.758 Γ— 10⁹⁸(99-digit number)
17585043254251267248…78687031546017177599
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
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