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Home/Chain Registry/Block #1,828,594

Block #1,828,594

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2016, 4:57:02 AM Β· Difficulty 10.7474 Β· 5,015,946 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65ae975dd01f589f435bc5b09f0c49f250dde52fa6f1dbaf97e08e5a62b53409
View on Chainz β†—

Difficulty

10.747431

Transactions

1

Size

200 B

Version

2

Bits

0abf57a4

Nonce

1,749,780,605

Timestamp

10/30/2016, 4:57:02 AM

Confirmations

5,015,946

Merkle Root

e47bdbc0d5d05ec7184434261c2e4c68047c5260ba10a713bde4d5de6edaf41a
Transactions (1)
Coinbasee47bdbc0d5d05e…e4d5de6edaf41a
1 in β†’ 1 out8.6400 XPM109 B
ARkxHpXn…MMkiRY2N
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.

5.501 Γ— 10⁹⁷(98-digit number)
55012503297810429686…54759893383665090560
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
5.501 Γ— 10⁹⁷(98-digit number)
55012503297810429686…54759893383665090559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.501 Γ— 10⁹⁷(98-digit number)
55012503297810429686…54759893383665090561
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
1.100 Γ— 10⁹⁸(99-digit number)
11002500659562085937…09519786767330181119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.100 Γ— 10⁹⁸(99-digit number)
11002500659562085937…09519786767330181121
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
2.200 Γ— 10⁹⁸(99-digit number)
22005001319124171874…19039573534660362239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.200 Γ— 10⁹⁸(99-digit number)
22005001319124171874…19039573534660362241
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
4.401 Γ— 10⁹⁸(99-digit number)
44010002638248343749…38079147069320724479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.401 Γ— 10⁹⁸(99-digit number)
44010002638248343749…38079147069320724481
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
8.802 Γ— 10⁹⁸(99-digit number)
88020005276496687499…76158294138641448959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.802 Γ— 10⁹⁸(99-digit number)
88020005276496687499…76158294138641448961
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 1828594

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 65ae975dd01f589f435bc5b09f0c49f250dde52fa6f1dbaf97e08e5a62b53409

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 #1,828,594 on Chainz β†—
Circulating Supply:58,000,723 XPMΒ·at block #6,844,539 Β· updates every 60s
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