XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,133,330

Block #2,133,330

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 10:42:15 AM Β· Difficulty 10.9097 Β· 4,708,252 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7d92eaf285c4c4d37016fcd401997c279ac8536e21fe19aa8ca57d0d3d357160
View on Chainz β†—

Difficulty

10.909687

Transactions

1

Size

199 B

Version

2

Bits

0ae8e13c

Nonce

150,179,054

Timestamp

5/26/2017, 10:42:15 AM

Confirmations

4,708,252

Merkle Root

24062aa2049a9a62395e8c10556945fb9c75d93fad112e6082b04a4193bb4283
Transactions (1)
Coinbase24062aa2049a9a…b04a4193bb4283
1 in β†’ 1 out8.3900 XPM109 B
AX21Stvg…QA7s5hyd
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.

3.955 Γ— 10⁹⁴(95-digit number)
39559855427697533328…52533953141377332800
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
3.955 Γ— 10⁹⁴(95-digit number)
39559855427697533328…52533953141377332799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.955 Γ— 10⁹⁴(95-digit number)
39559855427697533328…52533953141377332801
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
7.911 Γ— 10⁹⁴(95-digit number)
79119710855395066657…05067906282754665599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.911 Γ— 10⁹⁴(95-digit number)
79119710855395066657…05067906282754665601
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
1.582 Γ— 10⁹⁡(96-digit number)
15823942171079013331…10135812565509331199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.582 Γ— 10⁹⁡(96-digit number)
15823942171079013331…10135812565509331201
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
3.164 Γ— 10⁹⁡(96-digit number)
31647884342158026663…20271625131018662399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.164 Γ— 10⁹⁡(96-digit number)
31647884342158026663…20271625131018662401
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
6.329 Γ— 10⁹⁡(96-digit number)
63295768684316053326…40543250262037324799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.329 Γ— 10⁹⁡(96-digit number)
63295768684316053326…40543250262037324801
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
1.265 Γ— 10⁹⁢(97-digit number)
12659153736863210665…81086500524074649599
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 2133330

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 7d92eaf285c4c4d37016fcd401997c279ac8536e21fe19aa8ca57d0d3d357160

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 #2,133,330 on Chainz β†—
Circulating Supply:57,977,042 XPMΒ·at block #6,841,581 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy