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Block #1,812,329

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/18/2016, 9:22:33 AM Β· Difficulty 10.7815 Β· 4,986,901 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7033f49383be22c88d708841a582b5800f8a4cc797f50707d09a518ecccb0c25
View on Chainz β†—

Difficulty

10.781510

Transactions

1

Size

200 B

Version

2

Bits

0ac81105

Nonce

694,482,062

Timestamp

10/18/2016, 9:22:33 AM

Confirmations

4,986,901

Merkle Root

4c5ccd3222329eeccab5b7673cad851373b98e35c277f1f8a824460fac3a8637
Transactions (1)
Coinbase4c5ccd3222329e…24460fac3a8637
1 in β†’ 1 out8.5900 XPM110 B
AdKyLaYn…qyc2hcNw
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.

1.215 Γ— 10⁹⁡(96-digit number)
12153238784864895386…21132422796447117720
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
1.215 Γ— 10⁹⁡(96-digit number)
12153238784864895386…21132422796447117719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.215 Γ— 10⁹⁡(96-digit number)
12153238784864895386…21132422796447117721
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
2.430 Γ— 10⁹⁡(96-digit number)
24306477569729790773…42264845592894235439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.430 Γ— 10⁹⁡(96-digit number)
24306477569729790773…42264845592894235441
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
4.861 Γ— 10⁹⁡(96-digit number)
48612955139459581546…84529691185788470879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.861 Γ— 10⁹⁡(96-digit number)
48612955139459581546…84529691185788470881
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
9.722 Γ— 10⁹⁡(96-digit number)
97225910278919163092…69059382371576941759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.722 Γ— 10⁹⁡(96-digit number)
97225910278919163092…69059382371576941761
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
1.944 Γ— 10⁹⁢(97-digit number)
19445182055783832618…38118764743153883519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.944 Γ— 10⁹⁢(97-digit number)
19445182055783832618…38118764743153883521
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 1812329

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 7033f49383be22c88d708841a582b5800f8a4cc797f50707d09a518ecccb0c25

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 #1,812,329 on Chainz β†—
Circulating Supply:57,637,883 XPMΒ·at block #6,799,229 Β· updates every 60s
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