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Home/Chain Registry/Block #3,251,248

Block #3,251,248

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/3/2019, 3:54:34 AM Β· Difficulty 10.9961 Β· 3,593,809 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6230f682137d0804d44d331ff6740579a8f02b047716f30f8e99fcc1dd632f9a
View on Chainz β†—

Difficulty

10.996091

Transactions

1

Size

201 B

Version

2

Bits

0afeffd1

Nonce

1,419,534,473

Timestamp

7/3/2019, 3:54:34 AM

Confirmations

3,593,809

Merkle Root

eb52316142a7f1dc2b79aac2d6e370dc4d03e9bf7fc8ddae4b47ba3a29549d0e
Transactions (1)
Coinbaseeb52316142a7f1…47ba3a29549d0e
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

2.366 Γ— 10⁹⁢(97-digit number)
23667836804533875989…27714017108495810560
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
2.366 Γ— 10⁹⁢(97-digit number)
23667836804533875989…27714017108495810559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.366 Γ— 10⁹⁢(97-digit number)
23667836804533875989…27714017108495810561
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
4.733 Γ— 10⁹⁢(97-digit number)
47335673609067751978…55428034216991621119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.733 Γ— 10⁹⁢(97-digit number)
47335673609067751978…55428034216991621121
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
9.467 Γ— 10⁹⁢(97-digit number)
94671347218135503957…10856068433983242239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.467 Γ— 10⁹⁢(97-digit number)
94671347218135503957…10856068433983242241
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
1.893 Γ— 10⁹⁷(98-digit number)
18934269443627100791…21712136867966484479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.893 Γ— 10⁹⁷(98-digit number)
18934269443627100791…21712136867966484481
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
3.786 Γ— 10⁹⁷(98-digit number)
37868538887254201582…43424273735932968959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.786 Γ— 10⁹⁷(98-digit number)
37868538887254201582…43424273735932968961
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
7.573 Γ— 10⁹⁷(98-digit number)
75737077774508403165…86848547471865937919
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 3251248

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 6230f682137d0804d44d331ff6740579a8f02b047716f30f8e99fcc1dd632f9a

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 #3,251,248 on Chainz β†—
Circulating Supply:58,004,880 XPMΒ·at block #6,845,056 Β· updates every 60s
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