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Home/Chain Registry/Block #2,807,675

Block #2,807,675

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/24/2018, 8:04:00 AM Β· Difficulty 11.6734 Β· 4,032,523 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c597f2618565f79dd71ef61f2fc7228d593dee1dfe040c1b72d7de953e0706db
View on Chainz β†—

Difficulty

11.673430

Transactions

2

Size

1.14 KB

Version

2

Bits

0bac65f0

Nonce

152,918,336

Timestamp

8/24/2018, 8:04:00 AM

Confirmations

4,032,523

Merkle Root

6b09043c1ac1650be53fe624a6db81c57aef2daede8e72865e2d28e939476bb4
Transactions (2)
Coinbase350f4692e9183d…8c7e1c3f2f0250
1 in β†’ 1 out7.3400 XPM110 B
APZ7y9HT…J7rzKArM
e9253cfc2345ba…aae2ee506a98b9
6 in β†’ 2 out184.0320 XPM967 B
ATLw4wqX…kGTEjXFmAVeg62J5…S3TD9HDq
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.

5.716 Γ— 10⁹³(94-digit number)
57160493072014033648…61543486948387809200
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
5.716 Γ— 10⁹³(94-digit number)
57160493072014033648…61543486948387809199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.716 Γ— 10⁹³(94-digit number)
57160493072014033648…61543486948387809201
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
1.143 Γ— 10⁹⁴(95-digit number)
11432098614402806729…23086973896775618399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.143 Γ— 10⁹⁴(95-digit number)
11432098614402806729…23086973896775618401
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
2.286 Γ— 10⁹⁴(95-digit number)
22864197228805613459…46173947793551236799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.286 Γ— 10⁹⁴(95-digit number)
22864197228805613459…46173947793551236801
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
4.572 Γ— 10⁹⁴(95-digit number)
45728394457611226918…92347895587102473599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.572 Γ— 10⁹⁴(95-digit number)
45728394457611226918…92347895587102473601
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
9.145 Γ— 10⁹⁴(95-digit number)
91456788915222453837…84695791174204947199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.145 Γ— 10⁹⁴(95-digit number)
91456788915222453837…84695791174204947201
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
1.829 Γ— 10⁹⁡(96-digit number)
18291357783044490767…69391582348409894399
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 2807675

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 c597f2618565f79dd71ef61f2fc7228d593dee1dfe040c1b72d7de953e0706db

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 #2,807,675 on Chainz β†—
Circulating Supply:57,965,910 XPMΒ·at block #6,840,197 Β· updates every 60s
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