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Block #206,663

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2013, 11:00:25 PM Β· Difficulty 9.9015 Β· 6,594,519 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
689ffd5f61cbe67182852715f8f4e62a75afa87eeae947bf5ac564c789dbea59
View on Chainz β†—

Height

#206,663

Difficulty

9.901459

Transactions

1

Size

198 B

Version

2

Bits

09e6c5fc

Nonce

72,272

Timestamp

10/12/2013, 11:00:25 PM

Confirmations

6,594,519

Merkle Root

8af18245d3053130999f5ec2ae279e69dc81b8aabce920735cdae0537f321e4c
Transactions (1)
Coinbase8af18245d30531…dae0537f321e4c
1 in β†’ 1 out10.1800 XPM109 B
AboLCEin…7XjxSAfu
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.

6.952 Γ— 10⁹¹(92-digit number)
69528434346640978144…46593809158978307580
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
6.952 Γ— 10⁹¹(92-digit number)
69528434346640978144…46593809158978307579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.952 Γ— 10⁹¹(92-digit number)
69528434346640978144…46593809158978307581
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
1.390 Γ— 10⁹²(93-digit number)
13905686869328195628…93187618317956615159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.390 Γ— 10⁹²(93-digit number)
13905686869328195628…93187618317956615161
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
2.781 Γ— 10⁹²(93-digit number)
27811373738656391257…86375236635913230319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.781 Γ— 10⁹²(93-digit number)
27811373738656391257…86375236635913230321
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
5.562 Γ— 10⁹²(93-digit number)
55622747477312782515…72750473271826460639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.562 Γ— 10⁹²(93-digit number)
55622747477312782515…72750473271826460641
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
1.112 Γ— 10⁹³(94-digit number)
11124549495462556503…45500946543652921279
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 206663

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 689ffd5f61cbe67182852715f8f4e62a75afa87eeae947bf5ac564c789dbea59

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 #206,663 on Chainz β†—
Circulating Supply:57,653,519 XPMΒ·at block #6,801,181 Β· updates every 60s
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