XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,817,974

Block #2,817,974

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2018, 5:35:46 AM Β· Difficulty 11.6966 Β· 4,013,814 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
849440ce17c7b48ed3c391caaa5c18e30b541d7b5ec0d194da1966fbb7c0c176
View on Chainz β†—

Difficulty

11.696633

Transactions

1

Size

199 B

Version

2

Bits

0bb25687

Nonce

268,808,237

Timestamp

8/31/2018, 5:35:46 AM

Confirmations

4,013,814

Merkle Root

524d1b1462c66d3101a9b20eae1d4ae375a203eca36d929a20d0e5c56e823132
Transactions (1)
Coinbase524d1b1462c66d…d0e5c56e823132
1 in β†’ 1 out7.3000 XPM110 B
AHo1jVYt…5Z8n4x1V
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.

4.476 Γ— 10⁹²(93-digit number)
44764130504700525258…59072704123392189080
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.476 Γ— 10⁹²(93-digit number)
44764130504700525258…59072704123392189079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.476 Γ— 10⁹²(93-digit number)
44764130504700525258…59072704123392189081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
8.952 Γ— 10⁹²(93-digit number)
89528261009401050516…18145408246784378159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.952 Γ— 10⁹²(93-digit number)
89528261009401050516…18145408246784378161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.790 Γ— 10⁹³(94-digit number)
17905652201880210103…36290816493568756319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.790 Γ— 10⁹³(94-digit number)
17905652201880210103…36290816493568756321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.581 Γ— 10⁹³(94-digit number)
35811304403760420206…72581632987137512639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.581 Γ— 10⁹³(94-digit number)
35811304403760420206…72581632987137512641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
7.162 Γ— 10⁹³(94-digit number)
71622608807520840413…45163265974275025279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.162 Γ— 10⁹³(94-digit number)
71622608807520840413…45163265974275025281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁴(95-digit number)
14324521761504168082…90326531948550050559
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 2817974

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 849440ce17c7b48ed3c391caaa5c18e30b541d7b5ec0d194da1966fbb7c0c176

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 #2,817,974 on Chainz β†—
Circulating Supply:57,898,418 XPMΒ·at block #6,831,787 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