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Home/Chain Registry/Block #2,924,927

Block #2,924,927

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 4:19:59 AM Β· Difficulty 11.3557 Β· 3,915,369 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b517af025c1bdbf00ca7647791edacc038395b53b3fd88ab7883803482adf720
View on Chainz β†—

Difficulty

11.355740

Transactions

1

Size

201 B

Version

2

Bits

0b5b11ce

Nonce

865,603,326

Timestamp

11/16/2018, 4:19:59 AM

Confirmations

3,915,369

Merkle Root

48b0232ab05c2ca165b0b1d877d48427198be62ccdcc739df888dc159906f0e9
Transactions (1)
Coinbase48b0232ab05c2c…88dc159906f0e9
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.

9.423 Γ— 10⁹⁢(97-digit number)
94234359014133050174…85259135588612986880
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
9.423 Γ— 10⁹⁢(97-digit number)
94234359014133050174…85259135588612986879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.423 Γ— 10⁹⁢(97-digit number)
94234359014133050174…85259135588612986881
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
1.884 Γ— 10⁹⁷(98-digit number)
18846871802826610034…70518271177225973759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.884 Γ— 10⁹⁷(98-digit number)
18846871802826610034…70518271177225973761
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
3.769 Γ— 10⁹⁷(98-digit number)
37693743605653220069…41036542354451947519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.769 Γ— 10⁹⁷(98-digit number)
37693743605653220069…41036542354451947521
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
7.538 Γ— 10⁹⁷(98-digit number)
75387487211306440139…82073084708903895039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.538 Γ— 10⁹⁷(98-digit number)
75387487211306440139…82073084708903895041
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
1.507 Γ— 10⁹⁸(99-digit number)
15077497442261288027…64146169417807790079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.507 Γ— 10⁹⁸(99-digit number)
15077497442261288027…64146169417807790081
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
3.015 Γ— 10⁹⁸(99-digit number)
30154994884522576055…28292338835615580159
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 2924927

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 b517af025c1bdbf00ca7647791edacc038395b53b3fd88ab7883803482adf720

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 #2,924,927 on Chainz β†—
Circulating Supply:57,966,684 XPMΒ·at block #6,840,295 Β· updates every 60s
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