XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,062,980

Block #3,062,980

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 2/21/2019, 7:02:44 PM Β· Difficulty 11.0102 Β· 3,779,198 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d78557f7c996f93eac4a95a0f1fa66f5d5214a115bbf2326469a2702eac22447
View on Chainz β†—

Difficulty

11.010219

Transactions

2

Size

574 B

Version

2

Bits

0b029db8

Nonce

952,686,004

Timestamp

2/21/2019, 7:02:44 PM

Confirmations

3,779,198

Merkle Root

66297afc86bad94fda4d39d6b4c0238aa6ef261cb5c4181e073e4893778b6035
Transactions (2)
Coinbase529d587ced8884…a4bb669e121d11
1 in β†’ 1 out8.2500 XPM109 B
AUhjokok…k5m93PZR
27638ea63883ce…a2ba1442f946e0
2 in β†’ 2 out589.6240 XPM374 B
AeTHTL7A…vT1872bkAVLF5Yvg…DRNfHri3
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.

1.491 Γ— 10⁹⁷(98-digit number)
14919045237482882870…35270004280891883520
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
1.491 Γ— 10⁹⁷(98-digit number)
14919045237482882870…35270004280891883519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.983 Γ— 10⁹⁷(98-digit number)
29838090474965765741…70540008561783767039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.967 Γ— 10⁹⁷(98-digit number)
59676180949931531482…41080017123567534079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁸(99-digit number)
11935236189986306296…82160034247135068159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁸(99-digit number)
23870472379972612593…64320068494270136319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.774 Γ— 10⁹⁸(99-digit number)
47740944759945225186…28640136988540272639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.548 Γ— 10⁹⁸(99-digit number)
95481889519890450372…57280273977080545279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.909 Γ— 10⁹⁹(100-digit number)
19096377903978090074…14560547954161090559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.819 Γ— 10⁹⁹(100-digit number)
38192755807956180149…29121095908322181119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.638 Γ— 10⁹⁹(100-digit number)
76385511615912360298…58242191816644362239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.527 Γ— 10¹⁰⁰(101-digit number)
15277102323182472059…16484383633288724479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.055 Γ— 10¹⁰⁰(101-digit number)
30554204646364944119…32968767266577448959
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 3062980

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock d78557f7c996f93eac4a95a0f1fa66f5d5214a115bbf2326469a2702eac22447

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #3,062,980 on Chainz β†—
Circulating Supply:57,981,815 XPMΒ·at block #6,842,177 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