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Home/Chain Registry/Block #3,412,470

Block #3,412,470

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2019, 6:50:14 AM Β· Difficulty 10.9850 Β· 3,433,156 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2af4a10c67316299a11781d6399d3c1225431c78223c67501be5d4cd68858d68
View on Chainz β†—

Difficulty

10.984955

Transactions

1

Size

201 B

Version

2

Bits

0afc2604

Nonce

539,140,637

Timestamp

10/30/2019, 6:50:14 AM

Confirmations

3,433,156

Merkle Root

b616420eaf4d07800f61ecedb3d2194f50052c6d08facab85aa3280103ca10e5
Transactions (1)
Coinbaseb616420eaf4d07…a3280103ca10e5
1 in β†’ 1 out8.2700 XPM109 B
Aa32y8PQ…e3Enbehj
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.

4.122 Γ— 10⁹⁸(99-digit number)
41226029006190328981…07716550153472081920
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
4.122 Γ— 10⁹⁸(99-digit number)
41226029006190328981…07716550153472081919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.122 Γ— 10⁹⁸(99-digit number)
41226029006190328981…07716550153472081921
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
8.245 Γ— 10⁹⁸(99-digit number)
82452058012380657963…15433100306944163839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.245 Γ— 10⁹⁸(99-digit number)
82452058012380657963…15433100306944163841
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
1.649 Γ— 10⁹⁹(100-digit number)
16490411602476131592…30866200613888327679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.649 Γ— 10⁹⁹(100-digit number)
16490411602476131592…30866200613888327681
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
3.298 Γ— 10⁹⁹(100-digit number)
32980823204952263185…61732401227776655359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.298 Γ— 10⁹⁹(100-digit number)
32980823204952263185…61732401227776655361
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
6.596 Γ— 10⁹⁹(100-digit number)
65961646409904526371…23464802455553310719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.596 Γ— 10⁹⁹(100-digit number)
65961646409904526371…23464802455553310721
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
1.319 Γ— 10¹⁰⁰(101-digit number)
13192329281980905274…46929604911106621439
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 3412470

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 2af4a10c67316299a11781d6399d3c1225431c78223c67501be5d4cd68858d68

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 #3,412,470 on Chainz β†—
Circulating Supply:58,009,456 XPMΒ·at block #6,845,625 Β· updates every 60s
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