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Home/Chain Registry/Block #1,312,371

Block #1,312,371

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/4/2015, 1:38:51 PM Β· Difficulty 10.8523 Β· 5,532,435 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c021a8e5f4eea782a10f28ae0765aeac5e391e8db0fea60e52db87b5a9d81250
View on Chainz β†—

Difficulty

10.852255

Transactions

1

Size

200 B

Version

2

Bits

0ada2d5f

Nonce

323,560,284

Timestamp

11/4/2015, 1:38:51 PM

Confirmations

5,532,435

Merkle Root

181befc27cafd78278902e86e24047fc2609d0713aad526aba0c05726abf7243
Transactions (1)
Coinbase181befc27cafd7…0c05726abf7243
1 in β†’ 1 out8.4800 XPM110 B
AU3CZDRi…4jDwpbcD
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.

7.544 Γ— 10⁹⁴(95-digit number)
75444123480565297286…17071080511852920320
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
7.544 Γ— 10⁹⁴(95-digit number)
75444123480565297286…17071080511852920319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.544 Γ— 10⁹⁴(95-digit number)
75444123480565297286…17071080511852920321
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
1.508 Γ— 10⁹⁡(96-digit number)
15088824696113059457…34142161023705840639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.508 Γ— 10⁹⁡(96-digit number)
15088824696113059457…34142161023705840641
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
3.017 Γ— 10⁹⁡(96-digit number)
30177649392226118914…68284322047411681279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.017 Γ— 10⁹⁡(96-digit number)
30177649392226118914…68284322047411681281
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
6.035 Γ— 10⁹⁡(96-digit number)
60355298784452237829…36568644094823362559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.035 Γ— 10⁹⁡(96-digit number)
60355298784452237829…36568644094823362561
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
1.207 Γ— 10⁹⁢(97-digit number)
12071059756890447565…73137288189646725119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.207 Γ— 10⁹⁢(97-digit number)
12071059756890447565…73137288189646725121
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 1312371

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 c021a8e5f4eea782a10f28ae0765aeac5e391e8db0fea60e52db87b5a9d81250

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 #1,312,371 on Chainz β†—
Circulating Supply:58,002,864 XPMΒ·at block #6,844,805 Β· updates every 60s
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