XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #340,878

Block #340,878

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/3/2014, 2:19:07 AM Β· Difficulty 10.1328 Β· 6,454,887 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8673d812e5338717f39fdec0da069bdc9bbad1a1fc7dadf0984d0dba427dcd84
View on Chainz β†—

Height

#340,878

Difficulty

10.132808

Transactions

1

Size

203 B

Version

2

Bits

0a21ffb0

Nonce

253,036

Timestamp

1/3/2014, 2:19:07 AM

Confirmations

6,454,887

Merkle Root

34a5d5ecebc7efbaa3df7d604bf4577e6b4c2c64eb8f796fc1ff3ba8ca95114f
Transactions (1)
Coinbase34a5d5ecebc7ef…ff3ba8ca95114f
1 in β†’ 1 out9.7200 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.795 Γ— 10¹⁰²(103-digit number)
17959201250994653843…15508121640837881600
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
1.795 Γ— 10¹⁰²(103-digit number)
17959201250994653843…15508121640837881599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.795 Γ— 10¹⁰²(103-digit number)
17959201250994653843…15508121640837881601
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
3.591 Γ— 10¹⁰²(103-digit number)
35918402501989307686…31016243281675763199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.591 Γ— 10¹⁰²(103-digit number)
35918402501989307686…31016243281675763201
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
7.183 Γ— 10¹⁰²(103-digit number)
71836805003978615372…62032486563351526399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.183 Γ— 10¹⁰²(103-digit number)
71836805003978615372…62032486563351526401
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
1.436 Γ— 10¹⁰³(104-digit number)
14367361000795723074…24064973126703052799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.436 Γ— 10¹⁰³(104-digit number)
14367361000795723074…24064973126703052801
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
2.873 Γ— 10¹⁰³(104-digit number)
28734722001591446148…48129946253406105599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.873 Γ— 10¹⁰³(104-digit number)
28734722001591446148…48129946253406105601
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 340878

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 8673d812e5338717f39fdec0da069bdc9bbad1a1fc7dadf0984d0dba427dcd84

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 #340,878 on Chainz β†—
Circulating Supply:57,610,202 XPMΒ·at block #6,795,764 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK