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Home/Chain Registry/Block #2,145,531

Block #2,145,531

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2017, 4:00:08 PM Β· Difficulty 10.8886 Β· 4,696,666 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e694c5ebdc1b92548fe4e4f79965d2eb319988e0d030a04099981183276e4432
View on Chainz β†—

Difficulty

10.888565

Transactions

1

Size

200 B

Version

2

Bits

0ae37901

Nonce

325,816,178

Timestamp

6/4/2017, 4:00:08 PM

Confirmations

4,696,666

Merkle Root

28cd9e1845700130757858ced8c1a7385b07a2f7ac3cc9c48c0796e9463f458f
Transactions (1)
Coinbase28cd9e18457001…0796e9463f458f
1 in β†’ 1 out8.4200 XPM110 B
AHaDoFf9…TppKLpnF
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.

4.984 Γ— 10⁹³(94-digit number)
49841956388340701427…55028312913248900640
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
4.984 Γ— 10⁹³(94-digit number)
49841956388340701427…55028312913248900639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.984 Γ— 10⁹³(94-digit number)
49841956388340701427…55028312913248900641
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
9.968 Γ— 10⁹³(94-digit number)
99683912776681402854…10056625826497801279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.968 Γ— 10⁹³(94-digit number)
99683912776681402854…10056625826497801281
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
1.993 Γ— 10⁹⁴(95-digit number)
19936782555336280570…20113251652995602559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.993 Γ— 10⁹⁴(95-digit number)
19936782555336280570…20113251652995602561
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
3.987 Γ— 10⁹⁴(95-digit number)
39873565110672561141…40226503305991205119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.987 Γ— 10⁹⁴(95-digit number)
39873565110672561141…40226503305991205121
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
7.974 Γ— 10⁹⁴(95-digit number)
79747130221345122283…80453006611982410239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.974 Γ— 10⁹⁴(95-digit number)
79747130221345122283…80453006611982410241
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
1.594 Γ— 10⁹⁡(96-digit number)
15949426044269024456…60906013223964820479
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 2145531

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 e694c5ebdc1b92548fe4e4f79965d2eb319988e0d030a04099981183276e4432

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 #2,145,531 on Chainz β†—
Circulating Supply:57,981,970 XPMΒ·at block #6,842,196 Β· updates every 60s
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