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Home/Chain Registry/Block #3,085,413

Block #3,085,413

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/9/2019, 12:47:22 PM Β· Difficulty 11.0323 Β· 3,753,853 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe47d3a1d5303c304769c4f0474a5e968acc5e975f6cbadfc0cada94c97f4139
View on Chainz β†—

Difficulty

11.032270

Transactions

2

Size

1.71 KB

Version

2

Bits

0b0842db

Nonce

801,072,096

Timestamp

3/9/2019, 12:47:22 PM

Confirmations

3,753,853

Merkle Root

4b32986ae34161c025ec341c8dd51a723b70972a8ea7a7c607c4ab6e9db659f5
Transactions (2)
Coinbase7f1d0ec87da603…7df8e8aef68658
1 in β†’ 1 out8.2200 XPM110 B
AUhjokok…k5m93PZR
3e6e2e58758fde…0e00b58922c880
10 in β†’ 2 out6159.2372 XPM1.52 KB
APup3g8X…S7W6vJHmAaBnRC14…ACmNV8D9
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.

9.962 Γ— 10⁹⁴(95-digit number)
99626377233000845094…32475702808070144000
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
9.962 Γ— 10⁹⁴(95-digit number)
99626377233000845094…32475702808070143999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.962 Γ— 10⁹⁴(95-digit number)
99626377233000845094…32475702808070144001
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
1.992 Γ— 10⁹⁡(96-digit number)
19925275446600169018…64951405616140287999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.992 Γ— 10⁹⁡(96-digit number)
19925275446600169018…64951405616140288001
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
3.985 Γ— 10⁹⁡(96-digit number)
39850550893200338037…29902811232280575999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.985 Γ— 10⁹⁡(96-digit number)
39850550893200338037…29902811232280576001
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
7.970 Γ— 10⁹⁡(96-digit number)
79701101786400676075…59805622464561151999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.970 Γ— 10⁹⁡(96-digit number)
79701101786400676075…59805622464561152001
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
1.594 Γ— 10⁹⁢(97-digit number)
15940220357280135215…19611244929122303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.594 Γ— 10⁹⁢(97-digit number)
15940220357280135215…19611244929122304001
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
3.188 Γ— 10⁹⁢(97-digit number)
31880440714560270430…39222489858244607999
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 3085413

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 fe47d3a1d5303c304769c4f0474a5e968acc5e975f6cbadfc0cada94c97f4139

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 #3,085,413 on Chainz β†—
Circulating Supply:57,958,411 XPMΒ·at block #6,839,265 Β· updates every 60s
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