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Block #791,080

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/31/2014, 7:03:29 PM Β· Difficulty 10.9733 Β· 6,014,148 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e3c5f0ccb623d6de48c8a32957192bbed0408ffd114da2e400ffa36f64ced18f
View on Chainz β†—

Height

#791,080

Difficulty

10.973281

Transactions

1

Size

243 B

Version

2

Bits

0af928f3

Nonce

508,910,282

Timestamp

10/31/2014, 7:03:29 PM

Confirmations

6,014,148

Merkle Root

e9198b08be2e53553ab7fc701f1e7243115ec1fc729175bc79e39e1a9a52a34c
Transactions (1)
Coinbasee9198b08be2e53…e39e1a9a52a34c
1 in β†’ 2 out8.2900 XPM152 B
AaTsfJ9E…nnwSZnUZALPu3s2c…EJXLjVFh
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.

1.045 Γ— 10⁹⁷(98-digit number)
10457019368526624117…58903659488279170560
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
1.045 Γ— 10⁹⁷(98-digit number)
10457019368526624117…58903659488279170559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.045 Γ— 10⁹⁷(98-digit number)
10457019368526624117…58903659488279170561
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
2.091 Γ— 10⁹⁷(98-digit number)
20914038737053248235…17807318976558341119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.091 Γ— 10⁹⁷(98-digit number)
20914038737053248235…17807318976558341121
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
4.182 Γ— 10⁹⁷(98-digit number)
41828077474106496471…35614637953116682239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.182 Γ— 10⁹⁷(98-digit number)
41828077474106496471…35614637953116682241
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
8.365 Γ— 10⁹⁷(98-digit number)
83656154948212992942…71229275906233364479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.365 Γ— 10⁹⁷(98-digit number)
83656154948212992942…71229275906233364481
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
1.673 Γ— 10⁹⁸(99-digit number)
16731230989642598588…42458551812466728959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.673 Γ— 10⁹⁸(99-digit number)
16731230989642598588…42458551812466728961
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 791080

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 e3c5f0ccb623d6de48c8a32957192bbed0408ffd114da2e400ffa36f64ced18f

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 #791,080 on Chainz β†—
Circulating Supply:57,685,897 XPMΒ·at block #6,805,227 Β· updates every 60s
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