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Home/Chain Registry/Block #2,833,203

Block #2,833,203

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 2:21:41 PM Β· Difficulty 11.7149 Β· 4,009,006 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27624d8d13fe363eab34a6d40bc2b6a8787363f0f7537c4658a5893a5a707060
View on Chainz β†—

Difficulty

11.714884

Transactions

1

Size

200 B

Version

2

Bits

0bb702a2

Nonce

1,333,840,035

Timestamp

9/10/2018, 2:21:41 PM

Confirmations

4,009,006

Merkle Root

1d269fb33f61d24ae378a376184084ab87d8e4a544f325deb9a271f7c8ccfc5b
Transactions (1)
Coinbase1d269fb33f61d2…a271f7c8ccfc5b
1 in β†’ 1 out7.2700 XPM110 B
AJotf4Z5…ntwseehJ
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.

2.093 Γ— 10⁹⁡(96-digit number)
20931442879243119401…50394911784324136960
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
2.093 Γ— 10⁹⁡(96-digit number)
20931442879243119401…50394911784324136959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.093 Γ— 10⁹⁡(96-digit number)
20931442879243119401…50394911784324136961
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
4.186 Γ— 10⁹⁡(96-digit number)
41862885758486238802…00789823568648273919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.186 Γ— 10⁹⁡(96-digit number)
41862885758486238802…00789823568648273921
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
8.372 Γ— 10⁹⁡(96-digit number)
83725771516972477604…01579647137296547839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.372 Γ— 10⁹⁡(96-digit number)
83725771516972477604…01579647137296547841
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
1.674 Γ— 10⁹⁢(97-digit number)
16745154303394495520…03159294274593095679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.674 Γ— 10⁹⁢(97-digit number)
16745154303394495520…03159294274593095681
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
3.349 Γ— 10⁹⁢(97-digit number)
33490308606788991041…06318588549186191359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.349 Γ— 10⁹⁢(97-digit number)
33490308606788991041…06318588549186191361
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
6.698 Γ— 10⁹⁢(97-digit number)
66980617213577982083…12637177098372382719
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 2833203

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 27624d8d13fe363eab34a6d40bc2b6a8787363f0f7537c4658a5893a5a707060

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 #2,833,203 on Chainz β†—
Circulating Supply:57,982,068 XPMΒ·at block #6,842,208 Β· updates every 60s
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