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Home/Chain Registry/Block #2,825,893

Block #2,825,893

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2018, 1:49:02 PM Β· Difficulty 11.7102 Β· 4,017,208 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ee8652067940a73deb02c0167b1c778b2091f2e20860e1b85d82bdbb8d8900f9
View on Chainz β†—

Difficulty

11.710232

Transactions

1

Size

201 B

Version

2

Bits

0bb5d1c8

Nonce

225,881,483

Timestamp

9/5/2018, 1:49:02 PM

Confirmations

4,017,208

Merkle Root

e40c3d1479875133ef91a4df348e561b468854b3e70c1673e099c94994af30d8
Transactions (1)
Coinbasee40c3d14798751…99c94994af30d8
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
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.

7.148 Γ— 10⁹⁡(96-digit number)
71482774290564784169…38301083105021607200
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
7.148 Γ— 10⁹⁡(96-digit number)
71482774290564784169…38301083105021607199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.148 Γ— 10⁹⁡(96-digit number)
71482774290564784169…38301083105021607201
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
1.429 Γ— 10⁹⁢(97-digit number)
14296554858112956833…76602166210043214399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.429 Γ— 10⁹⁢(97-digit number)
14296554858112956833…76602166210043214401
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
2.859 Γ— 10⁹⁢(97-digit number)
28593109716225913667…53204332420086428799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.859 Γ— 10⁹⁢(97-digit number)
28593109716225913667…53204332420086428801
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
5.718 Γ— 10⁹⁢(97-digit number)
57186219432451827335…06408664840172857599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.718 Γ— 10⁹⁢(97-digit number)
57186219432451827335…06408664840172857601
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
1.143 Γ— 10⁹⁷(98-digit number)
11437243886490365467…12817329680345715199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.143 Γ— 10⁹⁷(98-digit number)
11437243886490365467…12817329680345715201
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
2.287 Γ— 10⁹⁷(98-digit number)
22874487772980730934…25634659360691430399
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 2825893

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 ee8652067940a73deb02c0167b1c778b2091f2e20860e1b85d82bdbb8d8900f9

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 #2,825,893 on Chainz β†—
Circulating Supply:57,989,171 XPMΒ·at block #6,843,100 Β· updates every 60s
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