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Home/Chain Registry/Block #1,368,443

Block #1,368,443

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2015, 10:51:43 PM Β· Difficulty 10.8345 Β· 5,474,389 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70c85d551517cda27c19dd7362c719626405ef471c87f17f530c1098a0422e76
View on Chainz β†—

Difficulty

10.834454

Transactions

1

Size

200 B

Version

2

Bits

0ad59ec5

Nonce

47,153,443

Timestamp

12/13/2015, 10:51:43 PM

Confirmations

5,474,389

Merkle Root

2530068da40306270046b73c966227eb26f0c1a390f4edbebfc8466e33b6a263
Transactions (1)
Coinbase2530068da40306…c8466e33b6a263
1 in β†’ 1 out8.5100 XPM110 B
AG2HKwNG…u8geiFDE
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.

7.262 Γ— 10⁹⁴(95-digit number)
72628058759657109190…20450755934323276560
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
7.262 Γ— 10⁹⁴(95-digit number)
72628058759657109190…20450755934323276559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.262 Γ— 10⁹⁴(95-digit number)
72628058759657109190…20450755934323276561
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
1.452 Γ— 10⁹⁡(96-digit number)
14525611751931421838…40901511868646553119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.452 Γ— 10⁹⁡(96-digit number)
14525611751931421838…40901511868646553121
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
2.905 Γ— 10⁹⁡(96-digit number)
29051223503862843676…81803023737293106239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.905 Γ— 10⁹⁡(96-digit number)
29051223503862843676…81803023737293106241
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
5.810 Γ— 10⁹⁡(96-digit number)
58102447007725687352…63606047474586212479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.810 Γ— 10⁹⁡(96-digit number)
58102447007725687352…63606047474586212481
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
1.162 Γ— 10⁹⁢(97-digit number)
11620489401545137470…27212094949172424959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.162 Γ— 10⁹⁢(97-digit number)
11620489401545137470…27212094949172424961
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 1368443

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 70c85d551517cda27c19dd7362c719626405ef471c87f17f530c1098a0422e76

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 #1,368,443 on Chainz β†—
Circulating Supply:57,986,999 XPMΒ·at block #6,842,831 Β· updates every 60s
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