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Home/Chain Registry/Block #1,585,945

Block #1,585,945

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2016, 5:42:42 PM Β· Difficulty 10.6489 Β· 5,256,237 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4f5457ef1b68c3f3f7af18711eb72ef61a352eae29ca09d2350dbdacd4bebc7e
View on Chainz β†—

Difficulty

10.648852

Transactions

1

Size

200 B

Version

2

Bits

0aa61b24

Nonce

274,738,087

Timestamp

5/15/2016, 5:42:42 PM

Confirmations

5,256,237

Merkle Root

e28a43a1973ec494e42e12bf9ffe43d646e25bc2dda5d4e29f7e2e3b44d88177
Transactions (1)
Coinbasee28a43a1973ec4…7e2e3b44d88177
1 in β†’ 1 out8.8000 XPM110 B
AWfiAjw6…vQoG7zKr
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.

4.329 Γ— 10⁹⁴(95-digit number)
43295701524147512153…71902399913564679100
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
4.329 Γ— 10⁹⁴(95-digit number)
43295701524147512153…71902399913564679099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.329 Γ— 10⁹⁴(95-digit number)
43295701524147512153…71902399913564679101
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
8.659 Γ— 10⁹⁴(95-digit number)
86591403048295024307…43804799827129358199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.659 Γ— 10⁹⁴(95-digit number)
86591403048295024307…43804799827129358201
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
1.731 Γ— 10⁹⁡(96-digit number)
17318280609659004861…87609599654258716399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.731 Γ— 10⁹⁡(96-digit number)
17318280609659004861…87609599654258716401
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
3.463 Γ— 10⁹⁡(96-digit number)
34636561219318009722…75219199308517432799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.463 Γ— 10⁹⁡(96-digit number)
34636561219318009722…75219199308517432801
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
6.927 Γ— 10⁹⁡(96-digit number)
69273122438636019445…50438398617034865599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.927 Γ— 10⁹⁡(96-digit number)
69273122438636019445…50438398617034865601
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 1585945

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 4f5457ef1b68c3f3f7af18711eb72ef61a352eae29ca09d2350dbdacd4bebc7e

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 #1,585,945 on Chainz β†—
Circulating Supply:57,981,848 XPMΒ·at block #6,842,181 Β· updates every 60s
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