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Home/Chain Registry/Block #1,719,304

Block #1,719,304

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2016, 4:23:29 AM Β· Difficulty 10.6706 Β· 5,076,610 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a75192a1702ca4f504d29fd4d77955cd0526545cd0a2986127ae545b6cdd5a0
View on Chainz β†—

Difficulty

10.670592

Transactions

1

Size

201 B

Version

2

Bits

0aababf1

Nonce

286,642,480

Timestamp

8/16/2016, 4:23:29 AM

Confirmations

5,076,610

Merkle Root

7abe20650c7fd0e7c082d8a5d3618cc4fd1a3dfc26b48173dda611123d6ea0df
Transactions (1)
Coinbase7abe20650c7fd0…a611123d6ea0df
1 in β†’ 1 out8.7700 XPM110 B
AYCdTYrb…1urVgpK6
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.

1.297 Γ— 10⁹⁸(99-digit number)
12978929552625323216…53819672632188518400
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
1.297 Γ— 10⁹⁸(99-digit number)
12978929552625323216…53819672632188518399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.297 Γ— 10⁹⁸(99-digit number)
12978929552625323216…53819672632188518401
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
2.595 Γ— 10⁹⁸(99-digit number)
25957859105250646433…07639345264377036799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.595 Γ— 10⁹⁸(99-digit number)
25957859105250646433…07639345264377036801
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
5.191 Γ— 10⁹⁸(99-digit number)
51915718210501292867…15278690528754073599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.191 Γ— 10⁹⁸(99-digit number)
51915718210501292867…15278690528754073601
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
1.038 Γ— 10⁹⁹(100-digit number)
10383143642100258573…30557381057508147199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.038 Γ— 10⁹⁹(100-digit number)
10383143642100258573…30557381057508147201
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
2.076 Γ— 10⁹⁹(100-digit number)
20766287284200517146…61114762115016294399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.076 Γ— 10⁹⁹(100-digit number)
20766287284200517146…61114762115016294401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.153 Γ— 10⁹⁹(100-digit number)
41532574568401034293…22229524230032588799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1719304

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 1a75192a1702ca4f504d29fd4d77955cd0526545cd0a2986127ae545b6cdd5a0

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 #1,719,304 on Chainz β†—
Circulating Supply:57,611,398 XPMΒ·at block #6,795,913 Β· updates every 60s
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