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Block #340,223

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/2/2014, 3:36:27 PM Β· Difficulty 10.1302 Β· 6,460,136 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef8d359eb28ad72a98e34f48f92afc6964fde52ce782519c1e358b477d65d22c
View on Chainz β†—

Height

#340,223

Difficulty

10.130167

Transactions

1

Size

201 B

Version

2

Bits

0a21529f

Nonce

69,135

Timestamp

1/2/2014, 3:36:27 PM

Confirmations

6,460,136

Merkle Root

c81b2df509734c56699ef42b5f6f01366b64100fa7a973a832a4794b734d60b3
Transactions (1)
Coinbasec81b2df509734c…a4794b734d60b3
1 in β†’ 1 out9.7300 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.

7.557 Γ— 10⁹⁷(98-digit number)
75575179477439128621…77953249993133198080
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
7.557 Γ— 10⁹⁷(98-digit number)
75575179477439128621…77953249993133198079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.557 Γ— 10⁹⁷(98-digit number)
75575179477439128621…77953249993133198081
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
1.511 Γ— 10⁹⁸(99-digit number)
15115035895487825724…55906499986266396159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.511 Γ— 10⁹⁸(99-digit number)
15115035895487825724…55906499986266396161
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
3.023 Γ— 10⁹⁸(99-digit number)
30230071790975651448…11812999972532792319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.023 Γ— 10⁹⁸(99-digit number)
30230071790975651448…11812999972532792321
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
6.046 Γ— 10⁹⁸(99-digit number)
60460143581951302897…23625999945065584639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.046 Γ— 10⁹⁸(99-digit number)
60460143581951302897…23625999945065584641
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
1.209 Γ— 10⁹⁹(100-digit number)
12092028716390260579…47251999890131169279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.209 Γ— 10⁹⁹(100-digit number)
12092028716390260579…47251999890131169281
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 340223

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 ef8d359eb28ad72a98e34f48f92afc6964fde52ce782519c1e358b477d65d22c

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 #340,223 on Chainz β†—
Circulating Supply:57,646,930 XPMΒ·at block #6,800,358 Β· updates every 60s
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