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Home/Chain Registry/Block #2,097,438

Block #2,097,438

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2017, 5:07:10 PM Β· Difficulty 10.8716 Β· 4,729,574 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
50c14b3c15b1832a5c7550c3313cd0826d16edbab1247abdaecb892fa567aac4
View on Chainz β†—

Difficulty

10.871583

Transactions

1

Size

202 B

Version

2

Bits

0adf2009

Nonce

161,732,595

Timestamp

5/2/2017, 5:07:10 PM

Confirmations

4,729,574

Merkle Root

c39821947d4e48b4c60b70c62c7d4d5143f31f6a1cd497d1c86e4971768443ab
Transactions (1)
Coinbasec39821947d4e48…6e4971768443ab
1 in β†’ 1 out8.4500 XPM110 B
ASbpvUdx…fQzKKJUS
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.

2.632 Γ— 10⁹⁸(99-digit number)
26327048297775616703…33839461475372236800
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
2.632 Γ— 10⁹⁸(99-digit number)
26327048297775616703…33839461475372236799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.632 Γ— 10⁹⁸(99-digit number)
26327048297775616703…33839461475372236801
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
5.265 Γ— 10⁹⁸(99-digit number)
52654096595551233407…67678922950744473599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.265 Γ— 10⁹⁸(99-digit number)
52654096595551233407…67678922950744473601
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
1.053 Γ— 10⁹⁹(100-digit number)
10530819319110246681…35357845901488947199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.053 Γ— 10⁹⁹(100-digit number)
10530819319110246681…35357845901488947201
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
2.106 Γ— 10⁹⁹(100-digit number)
21061638638220493362…70715691802977894399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.106 Γ— 10⁹⁹(100-digit number)
21061638638220493362…70715691802977894401
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
4.212 Γ— 10⁹⁹(100-digit number)
42123277276440986725…41431383605955788799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.212 Γ— 10⁹⁹(100-digit number)
42123277276440986725…41431383605955788801
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 2097438

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 50c14b3c15b1832a5c7550c3313cd0826d16edbab1247abdaecb892fa567aac4

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 #2,097,438 on Chainz β†—
Circulating Supply:57,860,273 XPMΒ·at block #6,827,011 Β· updates every 60s
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