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Home/Chain Registry/Block #2,792,326

Block #2,792,326

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2018, 3:38:20 PM Β· Difficulty 11.6752 Β· 4,040,300 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b198abfa95a7e6636d3b46c2a4ec7d3adaca7d8bf607a483fa8e56d46dea4b1e
View on Chainz β†—

Difficulty

11.675197

Transactions

1

Size

201 B

Version

2

Bits

0bacd9bc

Nonce

84,375,542

Timestamp

8/13/2018, 3:38:20 PM

Confirmations

4,040,300

Merkle Root

8c605e640e7b27ccf6a996e3c422ee0d62c5df41048db3ae812d121e23495faa
Transactions (1)
Coinbase8c605e640e7b27…2d121e23495faa
1 in β†’ 1 out7.3200 XPM110 B
AK34q7gj…fbReZhvh
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.

1.068 Γ— 10⁹⁢(97-digit number)
10689046739415248223…08175723322305771520
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
1.068 Γ— 10⁹⁢(97-digit number)
10689046739415248223…08175723322305771519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.068 Γ— 10⁹⁢(97-digit number)
10689046739415248223…08175723322305771521
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
2.137 Γ— 10⁹⁢(97-digit number)
21378093478830496446…16351446644611543039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.137 Γ— 10⁹⁢(97-digit number)
21378093478830496446…16351446644611543041
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
4.275 Γ— 10⁹⁢(97-digit number)
42756186957660992892…32702893289223086079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.275 Γ— 10⁹⁢(97-digit number)
42756186957660992892…32702893289223086081
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
8.551 Γ— 10⁹⁢(97-digit number)
85512373915321985784…65405786578446172159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.551 Γ— 10⁹⁢(97-digit number)
85512373915321985784…65405786578446172161
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
1.710 Γ— 10⁹⁷(98-digit number)
17102474783064397156…30811573156892344319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.710 Γ— 10⁹⁷(98-digit number)
17102474783064397156…30811573156892344321
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
3.420 Γ— 10⁹⁷(98-digit number)
34204949566128794313…61623146313784688639
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 2792326

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 b198abfa95a7e6636d3b46c2a4ec7d3adaca7d8bf607a483fa8e56d46dea4b1e

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 #2,792,326 on Chainz β†—
Circulating Supply:57,905,156 XPMΒ·at block #6,832,625 Β· updates every 60s
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