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Home/Chain Registry/Block #2,200,546

Block #2,200,546

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/10/2017, 1:37:31 AM Β· Difficulty 10.9511 Β· 4,644,773 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa3a7a137e3b94cf605dd30f2ba89f221d3bb7a000aa92a11e9169fd42492ce1
View on Chainz β†—

Difficulty

10.951144

Transactions

1

Size

199 B

Version

2

Bits

0af37e2b

Nonce

933,386,162

Timestamp

7/10/2017, 1:37:31 AM

Confirmations

4,644,773

Merkle Root

17be10823bd85f418a5f48bc6345f25b617b0c66ed399be82580e47aa7fcaf78
Transactions (1)
Coinbase17be10823bd85f…80e47aa7fcaf78
1 in β†’ 1 out8.3300 XPM109 B
AbWNwR4a…kosBAXf2
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.

7.384 Γ— 10⁹⁡(96-digit number)
73840305287469986100…47115373577618432000
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
7.384 Γ— 10⁹⁡(96-digit number)
73840305287469986100…47115373577618431999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.384 Γ— 10⁹⁡(96-digit number)
73840305287469986100…47115373577618432001
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
1.476 Γ— 10⁹⁢(97-digit number)
14768061057493997220…94230747155236863999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.476 Γ— 10⁹⁢(97-digit number)
14768061057493997220…94230747155236864001
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
2.953 Γ— 10⁹⁢(97-digit number)
29536122114987994440…88461494310473727999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.953 Γ— 10⁹⁢(97-digit number)
29536122114987994440…88461494310473728001
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
5.907 Γ— 10⁹⁢(97-digit number)
59072244229975988880…76922988620947455999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.907 Γ— 10⁹⁢(97-digit number)
59072244229975988880…76922988620947456001
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
1.181 Γ— 10⁹⁷(98-digit number)
11814448845995197776…53845977241894911999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.181 Γ— 10⁹⁷(98-digit number)
11814448845995197776…53845977241894912001
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 2200546

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 fa3a7a137e3b94cf605dd30f2ba89f221d3bb7a000aa92a11e9169fd42492ce1

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 #2,200,546 on Chainz β†—
Circulating Supply:58,006,990 XPMΒ·at block #6,845,318 Β· updates every 60s
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