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Block #309,348

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2013, 1:42:58 PM Β· Difficulty 9.9948 Β· 6,490,569 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e310b2e2d860b53e6060fe85841bdffd6e9307aa9311f655988db1c824320f80
View on Chainz β†—

Height

#309,348

Difficulty

9.994794

Transactions

1

Size

202 B

Version

2

Bits

09feaacf

Nonce

12,542

Timestamp

12/13/2013, 1:42:58 PM

Confirmations

6,490,569

Merkle Root

3701217e517732dc11425bcdefcdfec30f61cf77b215244b12ed04d40ad6d836
Transactions (1)
Coinbase3701217e517732…ed04d40ad6d836
1 in β†’ 1 out10.0000 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.

4.917 Γ— 10⁹⁸(99-digit number)
49170981762330687049…11014546210997684480
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
4.917 Γ— 10⁹⁸(99-digit number)
49170981762330687049…11014546210997684479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.917 Γ— 10⁹⁸(99-digit number)
49170981762330687049…11014546210997684481
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
9.834 Γ— 10⁹⁸(99-digit number)
98341963524661374098…22029092421995368959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.834 Γ— 10⁹⁸(99-digit number)
98341963524661374098…22029092421995368961
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
1.966 Γ— 10⁹⁹(100-digit number)
19668392704932274819…44058184843990737919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.966 Γ— 10⁹⁹(100-digit number)
19668392704932274819…44058184843990737921
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
3.933 Γ— 10⁹⁹(100-digit number)
39336785409864549639…88116369687981475839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.933 Γ— 10⁹⁹(100-digit number)
39336785409864549639…88116369687981475841
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
7.867 Γ— 10⁹⁹(100-digit number)
78673570819729099278…76232739375962951679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 309348

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 e310b2e2d860b53e6060fe85841bdffd6e9307aa9311f655988db1c824320f80

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 #309,348 on Chainz β†—
Circulating Supply:57,643,393 XPMΒ·at block #6,799,916 Β· updates every 60s
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