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Home/Chain Registry/Block #2,088,140

Block #2,088,140

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2017, 3:33:41 AM Β· Difficulty 10.8752 Β· 4,753,843 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5689bc480bf7b3836281f30aac062f4b0a6f1c68de77c872e9d8a37e953323b6
View on Chainz β†—

Difficulty

10.875188

Transactions

1

Size

199 B

Version

2

Bits

0ae00c4e

Nonce

794,866,713

Timestamp

4/26/2017, 3:33:41 AM

Confirmations

4,753,843

Merkle Root

09101bcb727c33fe7cf5b78a92edc47e8e8a53ac01f4a3ad557754c4007a02c7
Transactions (1)
Coinbase09101bcb727c33…7754c4007a02c7
1 in β†’ 1 out8.4400 XPM110 B
APG9i28k…1Y71yr53
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.

1.700 Γ— 10⁹³(94-digit number)
17003149557217501626…00838645660406917120
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
1.700 Γ— 10⁹³(94-digit number)
17003149557217501626…00838645660406917119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.700 Γ— 10⁹³(94-digit number)
17003149557217501626…00838645660406917121
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
3.400 Γ— 10⁹³(94-digit number)
34006299114435003252…01677291320813834239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.400 Γ— 10⁹³(94-digit number)
34006299114435003252…01677291320813834241
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
6.801 Γ— 10⁹³(94-digit number)
68012598228870006504…03354582641627668479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.801 Γ— 10⁹³(94-digit number)
68012598228870006504…03354582641627668481
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
1.360 Γ— 10⁹⁴(95-digit number)
13602519645774001300…06709165283255336959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.360 Γ— 10⁹⁴(95-digit number)
13602519645774001300…06709165283255336961
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
2.720 Γ— 10⁹⁴(95-digit number)
27205039291548002601…13418330566510673919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.720 Γ— 10⁹⁴(95-digit number)
27205039291548002601…13418330566510673921
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 2088140

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 5689bc480bf7b3836281f30aac062f4b0a6f1c68de77c872e9d8a37e953323b6

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 #2,088,140 on Chainz β†—
Circulating Supply:57,980,250 XPMΒ·at block #6,841,982 Β· updates every 60s
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