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Home/Chain Registry/Block #2,833,359

Block #2,833,359

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 4:44:36 PM Β· Difficulty 11.7156 Β· 4,009,909 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e532053f33e608ec0eaa188922f392d5599c312fa1aa2cdff59f601c3017041
View on Chainz β†—

Difficulty

11.715632

Transactions

2

Size

3.16 KB

Version

2

Bits

0bb733a7

Nonce

499,995,953

Timestamp

9/10/2018, 4:44:36 PM

Confirmations

4,009,909

Merkle Root

8f6c608296514d1d28640ee6819f110312bbeb4fba354411f1b39b80276a2357
Transactions (2)
Coinbase4f5677b4ae1baa…c00b2b33238668
1 in β†’ 1 out7.3100 XPM110 B
ATkH5ThT…S2BTqS95
02631efef66fc9…00a0a2cd1b79ba
20 in β†’ 2 out190.7600 XPM2.97 KB
ALh5G3Np…6TsNC2wjAf1iyJY1…ju517zGA
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.

8.916 Γ— 10⁹⁴(95-digit number)
89164730354146150119…05656819914779257520
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
8.916 Γ— 10⁹⁴(95-digit number)
89164730354146150119…05656819914779257519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.916 Γ— 10⁹⁴(95-digit number)
89164730354146150119…05656819914779257521
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
1.783 Γ— 10⁹⁡(96-digit number)
17832946070829230023…11313639829558515039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.783 Γ— 10⁹⁡(96-digit number)
17832946070829230023…11313639829558515041
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
3.566 Γ— 10⁹⁡(96-digit number)
35665892141658460047…22627279659117030079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.566 Γ— 10⁹⁡(96-digit number)
35665892141658460047…22627279659117030081
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
7.133 Γ— 10⁹⁡(96-digit number)
71331784283316920095…45254559318234060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.133 Γ— 10⁹⁡(96-digit number)
71331784283316920095…45254559318234060161
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
1.426 Γ— 10⁹⁢(97-digit number)
14266356856663384019…90509118636468120319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.426 Γ— 10⁹⁢(97-digit number)
14266356856663384019…90509118636468120321
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
2.853 Γ— 10⁹⁢(97-digit number)
28532713713326768038…81018237272936240639
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 2833359

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 7e532053f33e608ec0eaa188922f392d5599c312fa1aa2cdff59f601c3017041

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 #2,833,359 on Chainz β†—
Circulating Supply:57,990,518 XPMΒ·at block #6,843,267 Β· updates every 60s
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