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Home/Chain Registry/Block #2,133,327

Block #2,133,327

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 10:41:10 AM Β· Difficulty 10.9097 Β· 4,710,696 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c91edcef6a16b3a7d3413c9f8b5693774488550618fd65720354698b3b0a60de
View on Chainz β†—

Difficulty

10.909680

Transactions

2

Size

1.28 KB

Version

2

Bits

0ae8e0cc

Nonce

1,258,124,039

Timestamp

5/26/2017, 10:41:10 AM

Confirmations

4,710,696

Merkle Root

45370706d04893d8e136f3286911ab4abb2a59a59cd7086fa7ede4210aae22ba
Transactions (2)
Coinbasee019cf4a2da122…9cecd071e76acc
1 in β†’ 1 out8.4300 XPM109 B
AWSYbk4W…VcthMkhJ
676f7c3aa22a73…d5fa447221b3fd
7 in β†’ 2 out3533.6235 XPM1.09 KB
AeMVN4jn…FZ63C387ANicYbtS…Ws7nMMrk
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.

1.429 Γ— 10⁹⁡(96-digit number)
14295070137623545344…42574826352265646080
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
1.429 Γ— 10⁹⁡(96-digit number)
14295070137623545344…42574826352265646079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.429 Γ— 10⁹⁡(96-digit number)
14295070137623545344…42574826352265646081
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
2.859 Γ— 10⁹⁡(96-digit number)
28590140275247090688…85149652704531292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.859 Γ— 10⁹⁡(96-digit number)
28590140275247090688…85149652704531292161
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
5.718 Γ— 10⁹⁡(96-digit number)
57180280550494181377…70299305409062584319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.718 Γ— 10⁹⁡(96-digit number)
57180280550494181377…70299305409062584321
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
1.143 Γ— 10⁹⁢(97-digit number)
11436056110098836275…40598610818125168639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.143 Γ— 10⁹⁢(97-digit number)
11436056110098836275…40598610818125168641
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
2.287 Γ— 10⁹⁢(97-digit number)
22872112220197672551…81197221636250337279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.287 Γ— 10⁹⁢(97-digit number)
22872112220197672551…81197221636250337281
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 2133327

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 c91edcef6a16b3a7d3413c9f8b5693774488550618fd65720354698b3b0a60de

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 #2,133,327 on Chainz β†—
Circulating Supply:57,996,566 XPMΒ·at block #6,844,022 Β· updates every 60s
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