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Home/Chain Registry/Block #2,133,273

Block #2,133,273

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 9:36:58 AM Β· Difficulty 10.9098 Β· 4,711,515 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe8c0c6f8249868d1d32b108618bc862f2ae10b032610bb900017e99a6794ac3
View on Chainz β†—

Difficulty

10.909828

Transactions

1

Size

199 B

Version

2

Bits

0ae8ea7f

Nonce

883,009,520

Timestamp

5/26/2017, 9:36:58 AM

Confirmations

4,711,515

Merkle Root

ee0dfb3fa957589d1d275de61c848ecbe4be7e37202c312a144b0faf61bb1e8a
Transactions (1)
Coinbaseee0dfb3fa95758…4b0faf61bb1e8a
1 in β†’ 1 out8.3900 XPM110 B
ANBDjZmU…Kw1Kv7oP
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.

2.186 Γ— 10⁹³(94-digit number)
21865960217141424338…40745019935168378560
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
2.186 Γ— 10⁹³(94-digit number)
21865960217141424338…40745019935168378559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.186 Γ— 10⁹³(94-digit number)
21865960217141424338…40745019935168378561
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
4.373 Γ— 10⁹³(94-digit number)
43731920434282848676…81490039870336757119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.373 Γ— 10⁹³(94-digit number)
43731920434282848676…81490039870336757121
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
8.746 Γ— 10⁹³(94-digit number)
87463840868565697352…62980079740673514239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.746 Γ— 10⁹³(94-digit number)
87463840868565697352…62980079740673514241
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
1.749 Γ— 10⁹⁴(95-digit number)
17492768173713139470…25960159481347028479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.749 Γ— 10⁹⁴(95-digit number)
17492768173713139470…25960159481347028481
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
3.498 Γ— 10⁹⁴(95-digit number)
34985536347426278941…51920318962694056959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.498 Γ— 10⁹⁴(95-digit number)
34985536347426278941…51920318962694056961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2133273

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 fe8c0c6f8249868d1d32b108618bc862f2ae10b032610bb900017e99a6794ac3

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 #2,133,273 on Chainz β†—
Circulating Supply:58,002,716 XPMΒ·at block #6,844,787 Β· updates every 60s
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