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Home/Chain Registry/Block #1,341,115

Block #1,341,115

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2015, 1:33:52 PM Β· Difficulty 10.8026 Β· 5,503,895 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fda3eaef684700256e34dee13a5e4cef49372b20b7c71fcae914b3c1b9b1fc4d
View on Chainz β†—

Difficulty

10.802627

Transactions

1

Size

200 B

Version

2

Bits

0acd78f1

Nonce

287,213,894

Timestamp

11/25/2015, 1:33:52 PM

Confirmations

5,503,895

Merkle Root

e63ca8c5d7779ef35952b04bb8920d8a8451dac1eaf8233f70774f5e15f8efe3
Transactions (1)
Coinbasee63ca8c5d7779e…774f5e15f8efe3
1 in β†’ 1 out8.5600 XPM110 B
AVGS9bbK…jrCZ3wLq
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.

4.389 Γ— 10⁹⁡(96-digit number)
43898168597222867708…09103326416099409920
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
4.389 Γ— 10⁹⁡(96-digit number)
43898168597222867708…09103326416099409919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.389 Γ— 10⁹⁡(96-digit number)
43898168597222867708…09103326416099409921
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
8.779 Γ— 10⁹⁡(96-digit number)
87796337194445735416…18206652832198819839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.779 Γ— 10⁹⁡(96-digit number)
87796337194445735416…18206652832198819841
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
1.755 Γ— 10⁹⁢(97-digit number)
17559267438889147083…36413305664397639679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.755 Γ— 10⁹⁢(97-digit number)
17559267438889147083…36413305664397639681
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
3.511 Γ— 10⁹⁢(97-digit number)
35118534877778294166…72826611328795279359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.511 Γ— 10⁹⁢(97-digit number)
35118534877778294166…72826611328795279361
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
7.023 Γ— 10⁹⁢(97-digit number)
70237069755556588333…45653222657590558719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.023 Γ— 10⁹⁢(97-digit number)
70237069755556588333…45653222657590558721
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 1341115

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 fda3eaef684700256e34dee13a5e4cef49372b20b7c71fcae914b3c1b9b1fc4d

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 #1,341,115 on Chainz β†—
Circulating Supply:58,004,502 XPMΒ·at block #6,845,009 Β· updates every 60s
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