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Home/Chain Registry/Block #2,803,534

Block #2,803,534

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/21/2018, 12:55:25 PM Β· Difficulty 11.6659 Β· 4,037,936 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d5a84cdb8318436f5a904dbf86392ad674fea28b4cac97a2dbe186c1f44b4da
View on Chainz β†—

Difficulty

11.665885

Transactions

1

Size

200 B

Version

2

Bits

0baa7775

Nonce

1,847,947,511

Timestamp

8/21/2018, 12:55:25 PM

Confirmations

4,037,936

Merkle Root

e742525b0319f32f445cebdd0354009f7dd4c9644f17eb8fb897b7caf46fb7c1
Transactions (1)
Coinbasee742525b0319f3…97b7caf46fb7c1
1 in β†’ 1 out7.3400 XPM110 B
AMtEJDdH…CSg77SVf
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.

3.126 Γ— 10⁹⁴(95-digit number)
31265339660059879271…91264633374103783760
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
3.126 Γ— 10⁹⁴(95-digit number)
31265339660059879271…91264633374103783759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.126 Γ— 10⁹⁴(95-digit number)
31265339660059879271…91264633374103783761
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
6.253 Γ— 10⁹⁴(95-digit number)
62530679320119758542…82529266748207567519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.253 Γ— 10⁹⁴(95-digit number)
62530679320119758542…82529266748207567521
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
1.250 Γ— 10⁹⁡(96-digit number)
12506135864023951708…65058533496415135039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.250 Γ— 10⁹⁡(96-digit number)
12506135864023951708…65058533496415135041
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
2.501 Γ— 10⁹⁡(96-digit number)
25012271728047903417…30117066992830270079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.501 Γ— 10⁹⁡(96-digit number)
25012271728047903417…30117066992830270081
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
5.002 Γ— 10⁹⁡(96-digit number)
50024543456095806834…60234133985660540159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.002 Γ— 10⁹⁡(96-digit number)
50024543456095806834…60234133985660540161
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
1.000 Γ— 10⁹⁢(97-digit number)
10004908691219161366…20468267971321080319
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 2803534

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 8d5a84cdb8318436f5a904dbf86392ad674fea28b4cac97a2dbe186c1f44b4da

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 #2,803,534 on Chainz β†—
Circulating Supply:57,976,134 XPMΒ·at block #6,841,469 Β· updates every 60s
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