XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,719,820

Block #2,719,820

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/24/2018, 9:24:15 PM Β· Difficulty 11.6127 Β· 4,121,955 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
17a8073089c1284fc931ca84f814dbacf5757b42f391092d975a8b78695a6ed1
View on Chainz β†—

Difficulty

11.612686

Transactions

1

Size

200 B

Version

2

Bits

0b9cd903

Nonce

2,056,972,219

Timestamp

6/24/2018, 9:24:15 PM

Confirmations

4,121,955

Merkle Root

800936f82d272f5532df63647c3be6929be4877be3cf60cb303a05f2dc5482d5
Transactions (1)
Coinbase800936f82d272f…3a05f2dc5482d5
1 in β†’ 1 out7.4000 XPM110 B
Abss29iC…uuJV6Jb5
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.

1.003 Γ— 10⁹⁴(95-digit number)
10035159093707513122…57783829119526182320
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
1.003 Γ— 10⁹⁴(95-digit number)
10035159093707513122…57783829119526182319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.007 Γ— 10⁹⁴(95-digit number)
20070318187415026244…15567658239052364639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.014 Γ— 10⁹⁴(95-digit number)
40140636374830052488…31135316478104729279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.028 Γ— 10⁹⁴(95-digit number)
80281272749660104976…62270632956209458559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.605 Γ— 10⁹⁡(96-digit number)
16056254549932020995…24541265912418917119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.211 Γ— 10⁹⁡(96-digit number)
32112509099864041990…49082531824837834239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.422 Γ— 10⁹⁡(96-digit number)
64225018199728083981…98165063649675668479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.284 Γ— 10⁹⁢(97-digit number)
12845003639945616796…96330127299351336959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.569 Γ— 10⁹⁢(97-digit number)
25690007279891233592…92660254598702673919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.138 Γ— 10⁹⁢(97-digit number)
51380014559782467185…85320509197405347839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.027 Γ— 10⁹⁷(98-digit number)
10276002911956493437…70641018394810695679
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 2719820

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 17a8073089c1284fc931ca84f814dbacf5757b42f391092d975a8b78695a6ed1

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 #2,719,820 on Chainz β†—
Circulating Supply:57,978,577 XPMΒ·at block #6,841,774 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