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Home/Chain Registry/Block #1,403,097

Block #1,403,097

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2016, 2:39:48 PM Β· Difficulty 10.8051 Β· 5,440,161 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a0f574f89da7660051a4bb4bd706b3e1dbd74720dd96ff5ca23c8958b9379f1
View on Chainz β†—

Difficulty

10.805056

Transactions

1

Size

200 B

Version

2

Bits

0ace182a

Nonce

259,191,790

Timestamp

1/7/2016, 2:39:48 PM

Confirmations

5,440,161

Merkle Root

2660aa25a2ecbd3cba03ef6156b82bb7ccdc6594b7ac589ec6f028ce83d3b8e7
Transactions (1)
Coinbase2660aa25a2ecbd…f028ce83d3b8e7
1 in β†’ 1 out8.5500 XPM109 B
ANhHhGM3…4Tf4u4iR
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.

2.332 Γ— 10⁹⁢(97-digit number)
23329814373804805272…89493097144048400640
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
2.332 Γ— 10⁹⁢(97-digit number)
23329814373804805272…89493097144048400639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.332 Γ— 10⁹⁢(97-digit number)
23329814373804805272…89493097144048400641
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
4.665 Γ— 10⁹⁢(97-digit number)
46659628747609610544…78986194288096801279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.665 Γ— 10⁹⁢(97-digit number)
46659628747609610544…78986194288096801281
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
9.331 Γ— 10⁹⁢(97-digit number)
93319257495219221088…57972388576193602559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.331 Γ— 10⁹⁢(97-digit number)
93319257495219221088…57972388576193602561
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
1.866 Γ— 10⁹⁷(98-digit number)
18663851499043844217…15944777152387205119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.866 Γ— 10⁹⁷(98-digit number)
18663851499043844217…15944777152387205121
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
3.732 Γ— 10⁹⁷(98-digit number)
37327702998087688435…31889554304774410239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.732 Γ— 10⁹⁷(98-digit number)
37327702998087688435…31889554304774410241
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 1403097

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 5a0f574f89da7660051a4bb4bd706b3e1dbd74720dd96ff5ca23c8958b9379f1

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 #1,403,097 on Chainz β†—
Circulating Supply:57,990,437 XPMΒ·at block #6,843,257 Β· updates every 60s
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