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Home/Chain Registry/Block #2,134,405

Block #2,134,405

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/27/2017, 5:41:47 AM Β· Difficulty 10.9086 Β· 4,706,788 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e8692a7144cffb6a6e043ffdd89f0cd5d51b881483efe448e191951214f01788
View on Chainz β†—

Difficulty

10.908556

Transactions

1

Size

200 B

Version

2

Bits

0ae8971d

Nonce

1,047,734,662

Timestamp

5/27/2017, 5:41:47 AM

Confirmations

4,706,788

Merkle Root

d20ec238df4dd0650ea10b8a790b304cd4548cfed5a5c2308d1454a029acfbd9
Transactions (1)
Coinbased20ec238df4dd0…1454a029acfbd9
1 in β†’ 1 out8.3900 XPM110 B
AevNQeoj…TiPG7fHz
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.

2.361 Γ— 10⁹⁴(95-digit number)
23617980877226492300…53940087862033530880
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
2.361 Γ— 10⁹⁴(95-digit number)
23617980877226492300…53940087862033530879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.361 Γ— 10⁹⁴(95-digit number)
23617980877226492300…53940087862033530881
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
4.723 Γ— 10⁹⁴(95-digit number)
47235961754452984600…07880175724067061759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.723 Γ— 10⁹⁴(95-digit number)
47235961754452984600…07880175724067061761
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
9.447 Γ— 10⁹⁴(95-digit number)
94471923508905969200…15760351448134123519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.447 Γ— 10⁹⁴(95-digit number)
94471923508905969200…15760351448134123521
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
1.889 Γ— 10⁹⁡(96-digit number)
18894384701781193840…31520702896268247039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.889 Γ— 10⁹⁡(96-digit number)
18894384701781193840…31520702896268247041
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
3.778 Γ— 10⁹⁡(96-digit number)
37788769403562387680…63041405792536494079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.778 Γ— 10⁹⁡(96-digit number)
37788769403562387680…63041405792536494081
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 2134405

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 e8692a7144cffb6a6e043ffdd89f0cd5d51b881483efe448e191951214f01788

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 #2,134,405 on Chainz β†—
Circulating Supply:57,973,905 XPMΒ·at block #6,841,192 Β· updates every 60s
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