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Block #793,462

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/2/2014, 8:04:14 AM Β· Difficulty 10.9742 Β· 6,006,608 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f9d0f3fcb2183968759d1f3d2568ae82bc25a6872f76985f8100843dc4014d45
View on Chainz β†—

Height

#793,462

Difficulty

10.974205

Transactions

1

Size

208 B

Version

2

Bits

0af9657a

Nonce

98,034,342

Timestamp

11/2/2014, 8:04:14 AM

Confirmations

6,006,608

Merkle Root

95ed48109a217ab56850a3af2f1e7ccb0809ae7153fc0028cc60066d4f7af9bc
Transactions (1)
Coinbase95ed48109a217a…60066d4f7af9bc
1 in β†’ 1 out8.2900 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.

4.260 Γ— 10⁹⁹(100-digit number)
42600927872437103091…06617677876308213760
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
4.260 Γ— 10⁹⁹(100-digit number)
42600927872437103091…06617677876308213759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.260 Γ— 10⁹⁹(100-digit number)
42600927872437103091…06617677876308213761
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
8.520 Γ— 10⁹⁹(100-digit number)
85201855744874206183…13235355752616427519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.520 Γ— 10⁹⁹(100-digit number)
85201855744874206183…13235355752616427521
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
1.704 Γ— 10¹⁰⁰(101-digit number)
17040371148974841236…26470711505232855039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.704 Γ— 10¹⁰⁰(101-digit number)
17040371148974841236…26470711505232855041
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
3.408 Γ— 10¹⁰⁰(101-digit number)
34080742297949682473…52941423010465710079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.408 Γ— 10¹⁰⁰(101-digit number)
34080742297949682473…52941423010465710081
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
6.816 Γ— 10¹⁰⁰(101-digit number)
68161484595899364946…05882846020931420159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.816 Γ— 10¹⁰⁰(101-digit number)
68161484595899364946…05882846020931420161
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 793462

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 f9d0f3fcb2183968759d1f3d2568ae82bc25a6872f76985f8100843dc4014d45

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 #793,462 on Chainz β†—
Circulating Supply:57,644,624 XPMΒ·at block #6,800,069 Β· updates every 60s
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