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Home/Chain Registry/Block #1,438,057

Block #1,438,057

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/1/2016, 4:21:30 AM Β· Difficulty 10.7893 Β· 5,407,596 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
190b521457f76fe9767db01f51e9ebc976b31b133161e582fad715134747daf3
View on Chainz β†—

Difficulty

10.789326

Transactions

1

Size

200 B

Version

2

Bits

0aca1142

Nonce

176,559,626

Timestamp

2/1/2016, 4:21:30 AM

Confirmations

5,407,596

Merkle Root

a3a515cb7d3c7453de2923303057ebd9fcc2ba7d726bbf79ad2a5ea993da3f88
Transactions (1)
Coinbasea3a515cb7d3c74…2a5ea993da3f88
1 in β†’ 1 out8.5800 XPM109 B
AJqtZJ1w…5DKjitn7
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.

4.728 Γ— 10⁹⁢(97-digit number)
47288918561074597065…67427454933963571200
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
4.728 Γ— 10⁹⁢(97-digit number)
47288918561074597065…67427454933963571199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.728 Γ— 10⁹⁢(97-digit number)
47288918561074597065…67427454933963571201
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
9.457 Γ— 10⁹⁢(97-digit number)
94577837122149194131…34854909867927142399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.457 Γ— 10⁹⁢(97-digit number)
94577837122149194131…34854909867927142401
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
1.891 Γ— 10⁹⁷(98-digit number)
18915567424429838826…69709819735854284799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.891 Γ— 10⁹⁷(98-digit number)
18915567424429838826…69709819735854284801
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
3.783 Γ— 10⁹⁷(98-digit number)
37831134848859677652…39419639471708569599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.783 Γ— 10⁹⁷(98-digit number)
37831134848859677652…39419639471708569601
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
7.566 Γ— 10⁹⁷(98-digit number)
75662269697719355305…78839278943417139199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.566 Γ— 10⁹⁷(98-digit number)
75662269697719355305…78839278943417139201
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 1438057

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 190b521457f76fe9767db01f51e9ebc976b31b133161e582fad715134747daf3

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 #1,438,057 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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