XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,742,456

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/10/2018, 10:43:03 AM Β· Difficulty 11.6313 Β· 4,099,560 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6f119b5c6ed145af2ed013eda28fd7b880e2ea4934f18fd67e67cbeda9d24023
View on Chainz β†—

Height

#2,742,456

Difficulty

11.631294

Transactions

2

Size

574 B

Version

2

Bits

0ba19c79

Nonce

37,195,016

Timestamp

7/10/2018, 10:43:03 AM

Confirmations

4,099,560

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

7a54d77a04b7071a8014198c95f13d33d73adb3551821f73be1981ae26747cec
Transactions (2)
Coinbase42df80a22720d9…6698fda7a36864
1 in β†’ 1 out7.3900 XPM110 B
AZtxQr2F…7grUWrUz
39290830acc3f8…4996751aec6474
2 in β†’ 2 out100.7200 XPM374 B
AQSdoa2d…1tfzmmkbAdEdeNfU…UXZJg4Df
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.

5.249 Γ— 10⁹³(94-digit number)
52490501391638754266…32043697928775905919
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
5.249 Γ— 10⁹³(94-digit number)
52490501391638754266…32043697928775905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.049 Γ— 10⁹⁴(95-digit number)
10498100278327750853…64087395857551811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.099 Γ— 10⁹⁴(95-digit number)
20996200556655501706…28174791715103623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.199 Γ— 10⁹⁴(95-digit number)
41992401113311003412…56349583430207247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.398 Γ— 10⁹⁴(95-digit number)
83984802226622006825…12699166860414494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁡(96-digit number)
16796960445324401365…25398333720828989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.359 Γ— 10⁹⁡(96-digit number)
33593920890648802730…50796667441657978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.718 Γ— 10⁹⁡(96-digit number)
67187841781297605460…01593334883315957759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁢(97-digit number)
13437568356259521092…03186669766631915519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.687 Γ— 10⁹⁢(97-digit number)
26875136712519042184…06373339533263831039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.375 Γ— 10⁹⁢(97-digit number)
53750273425038084368…12746679066527662079
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:57,980,515 XPMΒ·at block #6,842,015 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