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Home/Chain Registry/Block #2,238,131

Block #2,238,131

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2017, 2:04:48 PM Β· Difficulty 10.9461 Β· 4,600,733 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa28a2f5c854197a17ed286c8064d1d25ac833498a628284264425d8b927fb0d
View on Chainz β†—

Difficulty

10.946094

Transactions

1

Size

200 B

Version

2

Bits

0af23337

Nonce

26,629,873

Timestamp

8/5/2017, 2:04:48 PM

Confirmations

4,600,733

Merkle Root

94084c2d91342a83033fbdb4972652fcdb93f3d2ef94164052e14351a5f99204
Transactions (1)
Coinbase94084c2d91342a…e14351a5f99204
1 in β†’ 1 out8.3300 XPM110 B
ASpCToKf…qoKCYuQz
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.

5.081 Γ— 10⁹⁡(96-digit number)
50810635846413241525…51180891536281040640
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
5.081 Γ— 10⁹⁡(96-digit number)
50810635846413241525…51180891536281040639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.081 Γ— 10⁹⁡(96-digit number)
50810635846413241525…51180891536281040641
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
1.016 Γ— 10⁹⁢(97-digit number)
10162127169282648305…02361783072562081279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.016 Γ— 10⁹⁢(97-digit number)
10162127169282648305…02361783072562081281
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
2.032 Γ— 10⁹⁢(97-digit number)
20324254338565296610…04723566145124162559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.032 Γ— 10⁹⁢(97-digit number)
20324254338565296610…04723566145124162561
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
4.064 Γ— 10⁹⁢(97-digit number)
40648508677130593220…09447132290248325119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.064 Γ— 10⁹⁢(97-digit number)
40648508677130593220…09447132290248325121
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
8.129 Γ— 10⁹⁢(97-digit number)
81297017354261186440…18894264580496650239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.129 Γ— 10⁹⁢(97-digit number)
81297017354261186440…18894264580496650241
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
1.625 Γ— 10⁹⁷(98-digit number)
16259403470852237288…37788529160993300479
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 2238131

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 fa28a2f5c854197a17ed286c8064d1d25ac833498a628284264425d8b927fb0d

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 #2,238,131 on Chainz β†—
Circulating Supply:57,955,177 XPMΒ·at block #6,838,863 Β· updates every 60s
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