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Home/Chain Registry/Block #2,118,695

Block #2,118,695

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2017, 6:50:45 AM Β· Difficulty 10.9091 Β· 4,724,423 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9571ef609cb5575cc6c32a910c06102e8b2b36df32f5c9b2f10f9c95cf412c86
View on Chainz β†—

Difficulty

10.909149

Transactions

2

Size

1.97 KB

Version

2

Bits

0ae8bdfa

Nonce

537,785,519

Timestamp

5/16/2017, 6:50:45 AM

Confirmations

4,724,423

Merkle Root

8c84847e6b1145941fe084b3a2cf38d7561e14c3adbcaa0f9237888576bfdefd
Transactions (2)
Coinbasecbba10e1d8a343…dfc81e9dd077f5
1 in β†’ 1 out8.4300 XPM109 B
APZy1ZqK…6F8f7Ejj
0d6921edb64558…82ab2c30e129c1
12 in β†’ 1 out1995.7393 XPM1.77 KB
AQZVhvkQ…55MyFfM2
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.

1.996 Γ— 10⁹⁡(96-digit number)
19960406025391319101…95133888996677075200
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
1.996 Γ— 10⁹⁡(96-digit number)
19960406025391319101…95133888996677075199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.996 Γ— 10⁹⁡(96-digit number)
19960406025391319101…95133888996677075201
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
3.992 Γ— 10⁹⁡(96-digit number)
39920812050782638202…90267777993354150399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.992 Γ— 10⁹⁡(96-digit number)
39920812050782638202…90267777993354150401
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
7.984 Γ— 10⁹⁡(96-digit number)
79841624101565276404…80535555986708300799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.984 Γ— 10⁹⁡(96-digit number)
79841624101565276404…80535555986708300801
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
1.596 Γ— 10⁹⁢(97-digit number)
15968324820313055280…61071111973416601599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15968324820313055280…61071111973416601601
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
3.193 Γ— 10⁹⁢(97-digit number)
31936649640626110561…22142223946833203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.193 Γ— 10⁹⁢(97-digit number)
31936649640626110561…22142223946833203201
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
6.387 Γ— 10⁹⁢(97-digit number)
63873299281252221123…44284447893666406399
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 2118695

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 9571ef609cb5575cc6c32a910c06102e8b2b36df32f5c9b2f10f9c95cf412c86

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 #2,118,695 on Chainz β†—
Circulating Supply:57,989,310 XPMΒ·at block #6,843,117 Β· updates every 60s
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