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Home/Chain Registry/Block #2,925,374

Block #2,925,374

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 11:54:11 AM Β· Difficulty 11.3549 Β· 3,915,661 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b623ec8454343844f9023e86c9f2277bc305e4d4982f9e8ed0ce697871d3ba73
View on Chainz β†—

Difficulty

11.354891

Transactions

1

Size

201 B

Version

2

Bits

0b5ada1d

Nonce

916,607,036

Timestamp

11/16/2018, 11:54:11 AM

Confirmations

3,915,661

Merkle Root

8f0dc20c9f12edd989f3185189c561fb89f25cd5a4ff9b4fdfc6283d382e0eab
Transactions (1)
Coinbase8f0dc20c9f12ed…c6283d382e0eab
1 in β†’ 1 out7.7400 XPM110 B
AUhjokok…k5m93PZR
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.

5.456 Γ— 10⁹⁷(98-digit number)
54566473885794526064…61978947248230891520
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
5.456 Γ— 10⁹⁷(98-digit number)
54566473885794526064…61978947248230891519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.456 Γ— 10⁹⁷(98-digit number)
54566473885794526064…61978947248230891521
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
1.091 Γ— 10⁹⁸(99-digit number)
10913294777158905212…23957894496461783039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.091 Γ— 10⁹⁸(99-digit number)
10913294777158905212…23957894496461783041
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
2.182 Γ— 10⁹⁸(99-digit number)
21826589554317810425…47915788992923566079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.182 Γ— 10⁹⁸(99-digit number)
21826589554317810425…47915788992923566081
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
4.365 Γ— 10⁹⁸(99-digit number)
43653179108635620851…95831577985847132159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.365 Γ— 10⁹⁸(99-digit number)
43653179108635620851…95831577985847132161
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
8.730 Γ— 10⁹⁸(99-digit number)
87306358217271241702…91663155971694264319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.730 Γ— 10⁹⁸(99-digit number)
87306358217271241702…91663155971694264321
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
1.746 Γ— 10⁹⁹(100-digit number)
17461271643454248340…83326311943388528639
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 2925374

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 b623ec8454343844f9023e86c9f2277bc305e4d4982f9e8ed0ce697871d3ba73

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 #2,925,374 on Chainz β†—
Circulating Supply:57,972,640 XPMΒ·at block #6,841,034 Β· updates every 60s
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