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Home/Chain Registry/Block #1,794,607

Block #1,794,607

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/6/2016, 4:43:32 AM Β· Difficulty 10.7737 Β· 5,032,396 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3307f047de55e5fb392f521f3ca8481ec189c32e24c05eba33083c2414cf7676
View on Chainz β†—

Difficulty

10.773652

Transactions

1

Size

242 B

Version

2

Bits

0ac60e11

Nonce

37,109,102

Timestamp

10/6/2016, 4:43:32 AM

Confirmations

5,032,396

Merkle Root

93b58329d02e40ca6a9af0240c8696c54a64c91e813c18902eecea48d8c06de3
Transactions (1)
Coinbase93b58329d02e40…ecea48d8c06de3
1 in β†’ 2 out8.6000 XPM152 B
AMdMLAA6…vZHXsifWALPu3s2c…EJXLjVFh
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.

1.477 Γ— 10⁹⁴(95-digit number)
14776198286043887595…03022772342111106480
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
1.477 Γ— 10⁹⁴(95-digit number)
14776198286043887595…03022772342111106479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.477 Γ— 10⁹⁴(95-digit number)
14776198286043887595…03022772342111106481
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
2.955 Γ— 10⁹⁴(95-digit number)
29552396572087775190…06045544684222212959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.955 Γ— 10⁹⁴(95-digit number)
29552396572087775190…06045544684222212961
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
5.910 Γ— 10⁹⁴(95-digit number)
59104793144175550380…12091089368444425919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.910 Γ— 10⁹⁴(95-digit number)
59104793144175550380…12091089368444425921
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
1.182 Γ— 10⁹⁡(96-digit number)
11820958628835110076…24182178736888851839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.182 Γ— 10⁹⁡(96-digit number)
11820958628835110076…24182178736888851841
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
2.364 Γ— 10⁹⁡(96-digit number)
23641917257670220152…48364357473777703679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.364 Γ— 10⁹⁡(96-digit number)
23641917257670220152…48364357473777703681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1794607

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 3307f047de55e5fb392f521f3ca8481ec189c32e24c05eba33083c2414cf7676

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 #1,794,607 on Chainz β†—
Circulating Supply:57,860,199 XPMΒ·at block #6,827,002 Β· updates every 60s
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