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Home/Chain Registry/Block #2,833,160

Block #2,833,160

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 1:39:25 PM Β· Difficulty 11.7148 Β· 4,009,717 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d321d43780f37348143fcd1d230bd422df9e0162bdc3b7211a71e2bd13e6543c
View on Chainz β†—

Difficulty

11.714800

Transactions

1

Size

200 B

Version

2

Bits

0bb6fd1d

Nonce

247,752,437

Timestamp

9/10/2018, 1:39:25 PM

Confirmations

4,009,717

Merkle Root

2766289da976a1ee4e3b565a166efe26760003a18790c0886e5cc514f7fcc031
Transactions (1)
Coinbase2766289da976a1…5cc514f7fcc031
1 in β†’ 1 out7.2700 XPM110 B
AYwU1ejp…oj6mtBXW
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.

1.541 Γ— 10⁹⁡(96-digit number)
15417128322702617039…71161167493838284800
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
1.541 Γ— 10⁹⁡(96-digit number)
15417128322702617039…71161167493838284799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.541 Γ— 10⁹⁡(96-digit number)
15417128322702617039…71161167493838284801
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
3.083 Γ— 10⁹⁡(96-digit number)
30834256645405234078…42322334987676569599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.083 Γ— 10⁹⁡(96-digit number)
30834256645405234078…42322334987676569601
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
6.166 Γ— 10⁹⁡(96-digit number)
61668513290810468156…84644669975353139199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.166 Γ— 10⁹⁡(96-digit number)
61668513290810468156…84644669975353139201
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
1.233 Γ— 10⁹⁢(97-digit number)
12333702658162093631…69289339950706278399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.233 Γ— 10⁹⁢(97-digit number)
12333702658162093631…69289339950706278401
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
2.466 Γ— 10⁹⁢(97-digit number)
24667405316324187262…38578679901412556799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.466 Γ— 10⁹⁢(97-digit number)
24667405316324187262…38578679901412556801
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
4.933 Γ— 10⁹⁢(97-digit number)
49334810632648374525…77157359802825113599
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 2833160

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 d321d43780f37348143fcd1d230bd422df9e0162bdc3b7211a71e2bd13e6543c

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 #2,833,160 on Chainz β†—
Circulating Supply:57,987,361 XPMΒ·at block #6,842,876 Β· updates every 60s
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