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Home/Chain Registry/Block #2,783,549

Block #2,783,549

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2018, 4:10:42 PM Β· Difficulty 11.6638 Β· 4,056,562 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46254ac48dd97b62803ef04f55db217ae720247410f1a0ced943cc07616fde3d
View on Chainz β†—

Difficulty

11.663783

Transactions

1

Size

200 B

Version

2

Bits

0ba9edaf

Nonce

1,993,374,580

Timestamp

8/7/2018, 4:10:42 PM

Confirmations

4,056,562

Merkle Root

b0e8be3639c88bdbb26cfffa443babb533cb5ff1cd94afcd17b6d0946eaea68e
Transactions (1)
Coinbaseb0e8be3639c88b…b6d0946eaea68e
1 in β†’ 1 out7.3400 XPM110 B
ASKpobHZ…SjR6Ur94
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.

5.195 Γ— 10⁹⁴(95-digit number)
51959318421698949654…54859383399676352960
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
5.195 Γ— 10⁹⁴(95-digit number)
51959318421698949654…54859383399676352959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.195 Γ— 10⁹⁴(95-digit number)
51959318421698949654…54859383399676352961
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
1.039 Γ— 10⁹⁡(96-digit number)
10391863684339789930…09718766799352705919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.039 Γ— 10⁹⁡(96-digit number)
10391863684339789930…09718766799352705921
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
2.078 Γ— 10⁹⁡(96-digit number)
20783727368679579861…19437533598705411839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.078 Γ— 10⁹⁡(96-digit number)
20783727368679579861…19437533598705411841
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
4.156 Γ— 10⁹⁡(96-digit number)
41567454737359159723…38875067197410823679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.156 Γ— 10⁹⁡(96-digit number)
41567454737359159723…38875067197410823681
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
8.313 Γ— 10⁹⁡(96-digit number)
83134909474718319446…77750134394821647359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.313 Γ— 10⁹⁡(96-digit number)
83134909474718319446…77750134394821647361
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
1.662 Γ— 10⁹⁢(97-digit number)
16626981894943663889…55500268789643294719
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 2783549

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 46254ac48dd97b62803ef04f55db217ae720247410f1a0ced943cc07616fde3d

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 #2,783,549 on Chainz β†—
Circulating Supply:57,965,200 XPMΒ·at block #6,840,110 Β· updates every 60s
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