XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,112,544

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/12/2017, 7:41:29 AM Β· Difficulty 10.9006 Β· 4,721,458 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
90f995739d99896af1ff23facd6e847b250f40a6a84a9449e50c006443603672
View on Chainz β†—

Height

#2,112,544

Difficulty

10.900631

Transactions

2

Size

1.54 KB

Version

2

Bits

0ae68fbe

Nonce

155,683,151

Timestamp

5/12/2017, 7:41:29 AM

Confirmations

4,721,458

Mined by

⛏️ P2SHAJnpy2mfH6HYwxqzaoScN7Xi89CY4RH8ME

Merkle Root

b75b987fb3be8c8a2c7b8b7c451a88fe779407498eee6813723efde93f45c5a8
Transactions (2)
Coinbased6a64c4111f420…e98e318d67139f
1 in β†’ 1 out8.4200 XPM110 B
AJnpy2mf…CY4RH8ME
3a81848997c3e5…e6c828f421247c
9 in β†’ 1 out103.4852 XPM1.35 KB
AHt1fopP…9Te6Ytwk
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.

8.349 Γ— 10⁹²(93-digit number)
83493516899853684912…21585747541410242079
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
8.349 Γ— 10⁹²(93-digit number)
83493516899853684912…21585747541410242079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.669 Γ— 10⁹³(94-digit number)
16698703379970736982…43171495082820484159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.339 Γ— 10⁹³(94-digit number)
33397406759941473964…86342990165640968319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.679 Γ— 10⁹³(94-digit number)
66794813519882947929…72685980331281936639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.335 Γ— 10⁹⁴(95-digit number)
13358962703976589585…45371960662563873279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.671 Γ— 10⁹⁴(95-digit number)
26717925407953179171…90743921325127746559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.343 Γ— 10⁹⁴(95-digit number)
53435850815906358343…81487842650255493119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.068 Γ— 10⁹⁡(96-digit number)
10687170163181271668…62975685300510986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.137 Γ— 10⁹⁡(96-digit number)
21374340326362543337…25951370601021972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.274 Γ— 10⁹⁡(96-digit number)
42748680652725086675…51902741202043944959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,916,243 XPMΒ·at block #6,834,001 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