XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,815,974

Block #2,815,974

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/29/2018, 11:10:38 PM Β· Difficulty 11.6859 Β· 4,017,883 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
01a4b87cbfcbe8af39d618752bcb0472afa4903b3065528d3b08ab28587d08f0
View on Chainz β†—

Difficulty

11.685919

Transactions

1

Size

201 B

Version

2

Bits

0baf9860

Nonce

45,354,591

Timestamp

8/29/2018, 11:10:38 PM

Confirmations

4,017,883

Merkle Root

207642f5a56d08e67532dfe6094f7eea5b61feaedd15f47a53f4a537849b003b
Transactions (1)
Coinbase207642f5a56d08…f4a537849b003b
1 in β†’ 1 out7.3100 XPM110 B
AR6L1ECu…uqxTbHUD
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.

3.905 Γ— 10⁹⁢(97-digit number)
39051690800789988273…82165047954584657920
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
3.905 Γ— 10⁹⁢(97-digit number)
39051690800789988273…82165047954584657919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.810 Γ— 10⁹⁢(97-digit number)
78103381601579976546…64330095909169315839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.562 Γ— 10⁹⁷(98-digit number)
15620676320315995309…28660191818338631679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.124 Γ— 10⁹⁷(98-digit number)
31241352640631990618…57320383636677263359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.248 Γ— 10⁹⁷(98-digit number)
62482705281263981236…14640767273354526719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.249 Γ— 10⁹⁸(99-digit number)
12496541056252796247…29281534546709053439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.499 Γ— 10⁹⁸(99-digit number)
24993082112505592494…58563069093418106879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.998 Γ— 10⁹⁸(99-digit number)
49986164225011184989…17126138186836213759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.997 Γ— 10⁹⁸(99-digit number)
99972328450022369979…34252276373672427519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.999 Γ— 10⁹⁹(100-digit number)
19994465690004473995…68504552747344855039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.998 Γ— 10⁹⁹(100-digit number)
39988931380008947991…37009105494689710079
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 2815974

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 01a4b87cbfcbe8af39d618752bcb0472afa4903b3065528d3b08ab28587d08f0

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 #2,815,974 on Chainz β†—
Circulating Supply:57,915,085 XPMΒ·at block #6,833,856 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