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Block #680,658

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2014, 9:22:30 PM Β· Difficulty 10.9624 Β· 6,115,073 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b80eb0d826176cb04a0b17bc76032707daaee75e843f59370b7e4673b6e97cbf
View on Chainz β†—

Height

#680,658

Difficulty

10.962446

Transactions

1

Size

206 B

Version

2

Bits

0af662da

Nonce

189,293,932

Timestamp

8/16/2014, 9:22:30 PM

Confirmations

6,115,073

Merkle Root

f974171fb01cf70e7eb1d6bd95d52d6779fb1de91a283ac8e47016e9283e1951
Transactions (1)
Coinbasef974171fb01cf7…7016e9283e1951
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.870 Γ— 10⁹⁡(96-digit number)
38701322681741742159…25309310849570603840
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
3.870 Γ— 10⁹⁡(96-digit number)
38701322681741742159…25309310849570603839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.870 Γ— 10⁹⁡(96-digit number)
38701322681741742159…25309310849570603841
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
7.740 Γ— 10⁹⁡(96-digit number)
77402645363483484318…50618621699141207679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.740 Γ— 10⁹⁡(96-digit number)
77402645363483484318…50618621699141207681
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
1.548 Γ— 10⁹⁢(97-digit number)
15480529072696696863…01237243398282415359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15480529072696696863…01237243398282415361
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
3.096 Γ— 10⁹⁢(97-digit number)
30961058145393393727…02474486796564830719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.096 Γ— 10⁹⁢(97-digit number)
30961058145393393727…02474486796564830721
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
6.192 Γ— 10⁹⁢(97-digit number)
61922116290786787454…04948973593129661439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.192 Γ— 10⁹⁢(97-digit number)
61922116290786787454…04948973593129661441
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 680658

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 b80eb0d826176cb04a0b17bc76032707daaee75e843f59370b7e4673b6e97cbf

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 #680,658 on Chainz β†—
Circulating Supply:57,609,924 XPMΒ·at block #6,795,730 Β· updates every 60s
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