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Home/Chain Registry/Block #1,853,194

Block #1,853,194

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2016, 1:43:10 PM Β· Difficulty 10.6368 Β· 4,988,021 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fbe8b3a26060bee1762c1482a4c34c3da423a6f660d3550f5b26b4a5fa853df7
View on Chainz β†—

Difficulty

10.636840

Transactions

1

Size

200 B

Version

2

Bits

0aa307fa

Nonce

543,986,522

Timestamp

11/17/2016, 1:43:10 PM

Confirmations

4,988,021

Merkle Root

118753c2120f94959169646a4e84df7385f1a902875a2eefbea24783bbae91c2
Transactions (1)
Coinbase118753c2120f94…a24783bbae91c2
1 in β†’ 1 out8.8200 XPM109 B
AQdzqhey…zjnU7pZ3
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.

9.043 Γ— 10⁹⁡(96-digit number)
90430051858478821335…53999412886024437120
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
9.043 Γ— 10⁹⁡(96-digit number)
90430051858478821335…53999412886024437119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.043 Γ— 10⁹⁡(96-digit number)
90430051858478821335…53999412886024437121
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
1.808 Γ— 10⁹⁢(97-digit number)
18086010371695764267…07998825772048874239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.808 Γ— 10⁹⁢(97-digit number)
18086010371695764267…07998825772048874241
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
3.617 Γ— 10⁹⁢(97-digit number)
36172020743391528534…15997651544097748479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.617 Γ— 10⁹⁢(97-digit number)
36172020743391528534…15997651544097748481
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
7.234 Γ— 10⁹⁢(97-digit number)
72344041486783057068…31995303088195496959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.234 Γ— 10⁹⁢(97-digit number)
72344041486783057068…31995303088195496961
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
1.446 Γ— 10⁹⁷(98-digit number)
14468808297356611413…63990606176390993919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.446 Γ— 10⁹⁷(98-digit number)
14468808297356611413…63990606176390993921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1853194

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 fbe8b3a26060bee1762c1482a4c34c3da423a6f660d3550f5b26b4a5fa853df7

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 #1,853,194 on Chainz β†—
Circulating Supply:57,974,079 XPMΒ·at block #6,841,214 Β· updates every 60s
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