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Home/Chain Registry/Block #2,130,323

Block #2,130,323

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 8:48:16 AM Β· Difficulty 10.9094 Β· 4,702,871 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
455c4c2bdc3a97e47fce979cee5ca9ba0327928d5aea11ec48ec7ee3d6234307
View on Chainz β†—

Difficulty

10.909376

Transactions

1

Size

201 B

Version

2

Bits

0ae8cce4

Nonce

528,888,290

Timestamp

5/24/2017, 8:48:16 AM

Confirmations

4,702,871

Merkle Root

b622e6ac46d3d7d56851b37d2fcd9cf878ed89015bbcae448b97c95b98182feb
Transactions (1)
Coinbaseb622e6ac46d3d7…97c95b98182feb
1 in β†’ 1 out8.3900 XPM110 B
Ac8vq2nh…p4iYBSS9
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.

1.772 Γ— 10⁹⁷(98-digit number)
17723801697077591519…67561905264943759360
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
1.772 Γ— 10⁹⁷(98-digit number)
17723801697077591519…67561905264943759359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.772 Γ— 10⁹⁷(98-digit number)
17723801697077591519…67561905264943759361
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
3.544 Γ— 10⁹⁷(98-digit number)
35447603394155183039…35123810529887518719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.544 Γ— 10⁹⁷(98-digit number)
35447603394155183039…35123810529887518721
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
7.089 Γ— 10⁹⁷(98-digit number)
70895206788310366078…70247621059775037439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.089 Γ— 10⁹⁷(98-digit number)
70895206788310366078…70247621059775037441
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
1.417 Γ— 10⁹⁸(99-digit number)
14179041357662073215…40495242119550074879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.417 Γ— 10⁹⁸(99-digit number)
14179041357662073215…40495242119550074881
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
2.835 Γ— 10⁹⁸(99-digit number)
28358082715324146431…80990484239100149759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.835 Γ— 10⁹⁸(99-digit number)
28358082715324146431…80990484239100149761
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 2130323

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 455c4c2bdc3a97e47fce979cee5ca9ba0327928d5aea11ec48ec7ee3d6234307

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 #2,130,323 on Chainz β†—
Circulating Supply:57,909,737 XPMΒ·at block #6,833,193 Β· updates every 60s
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