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Home/Chain Registry/Block #3,374,224

Block #3,374,224

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2019, 4:51:28 PM Β· Difficulty 10.9946 Β· 3,459,446 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
34a8c8dcecf6b09a8780ce42ed4b2d6b752adb9477a831f7244a69511c1119c0
View on Chainz β†—

Difficulty

10.994624

Transactions

2

Size

1.28 KB

Version

2

Bits

0afe9fb4

Nonce

506,822,437

Timestamp

9/29/2019, 4:51:28 PM

Confirmations

3,459,446

Merkle Root

e7c6912cd0880cf47dbd9a2cc1e1f968028b075a00698863f69c7a1dcf70a918
Transactions (2)
Coinbase4a41c25a8de2a8…52fe1bc7e66842
1 in β†’ 1 out8.2800 XPM109 B
ASiq2qtK…VMhmk7yL
b0916e540e8a20…d44738dfe0751f
7 in β†’ 2 out953.6330 XPM1.09 KB
AVK9cdsq…BENqpAtnAP2ikm3r…2qJRNrn6
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.

1.744 Γ— 10⁹⁡(96-digit number)
17440294260823696195…27856593537023734560
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
1.744 Γ— 10⁹⁡(96-digit number)
17440294260823696195…27856593537023734559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.744 Γ— 10⁹⁡(96-digit number)
17440294260823696195…27856593537023734561
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
3.488 Γ— 10⁹⁡(96-digit number)
34880588521647392390…55713187074047469119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.488 Γ— 10⁹⁡(96-digit number)
34880588521647392390…55713187074047469121
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
6.976 Γ— 10⁹⁡(96-digit number)
69761177043294784780…11426374148094938239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.976 Γ— 10⁹⁡(96-digit number)
69761177043294784780…11426374148094938241
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
1.395 Γ— 10⁹⁢(97-digit number)
13952235408658956956…22852748296189876479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.395 Γ— 10⁹⁢(97-digit number)
13952235408658956956…22852748296189876481
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
2.790 Γ— 10⁹⁢(97-digit number)
27904470817317913912…45705496592379752959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.790 Γ— 10⁹⁢(97-digit number)
27904470817317913912…45705496592379752961
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
5.580 Γ— 10⁹⁢(97-digit number)
55808941634635827824…91410993184759505919
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 3374224

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 34a8c8dcecf6b09a8780ce42ed4b2d6b752adb9477a831f7244a69511c1119c0

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 #3,374,224 on Chainz β†—
Circulating Supply:57,913,577 XPMΒ·at block #6,833,669 Β· updates every 60s
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