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Home/Chain Registry/Block #3,632,863

Block #3,632,863

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/7/2020, 10:01:39 AM Β· Difficulty 10.9042 Β· 3,208,482 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
61d1538621367fbdfb0b2caffd27b9201f7f0c11e328a524adcdc892de203534
View on Chainz β†—

Difficulty

10.904177

Transactions

1

Size

200 B

Version

2

Bits

0ae77824

Nonce

1,076,744,446

Timestamp

4/7/2020, 10:01:39 AM

Confirmations

3,208,482

Merkle Root

b7c9b1ae615a81ca0c38a94edca24cd8d07f905a06465152626c1791e8bcb502
Transactions (1)
Coinbaseb7c9b1ae615a81…6c1791e8bcb502
1 in β†’ 1 out8.4000 XPM109 B
AXfJqzUb…HXeXmjMz
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.

1.839 Γ— 10⁹⁷(98-digit number)
18398666860280374323…14353778479605606400
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
1.839 Γ— 10⁹⁷(98-digit number)
18398666860280374323…14353778479605606399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.839 Γ— 10⁹⁷(98-digit number)
18398666860280374323…14353778479605606401
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
3.679 Γ— 10⁹⁷(98-digit number)
36797333720560748646…28707556959211212799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.679 Γ— 10⁹⁷(98-digit number)
36797333720560748646…28707556959211212801
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
7.359 Γ— 10⁹⁷(98-digit number)
73594667441121497293…57415113918422425599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.359 Γ— 10⁹⁷(98-digit number)
73594667441121497293…57415113918422425601
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
1.471 Γ— 10⁹⁸(99-digit number)
14718933488224299458…14830227836844851199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.471 Γ— 10⁹⁸(99-digit number)
14718933488224299458…14830227836844851201
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
2.943 Γ— 10⁹⁸(99-digit number)
29437866976448598917…29660455673689702399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.943 Γ— 10⁹⁸(99-digit number)
29437866976448598917…29660455673689702401
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 3632863

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 61d1538621367fbdfb0b2caffd27b9201f7f0c11e328a524adcdc892de203534

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 #3,632,863 on Chainz β†—
Circulating Supply:57,975,126 XPMΒ·at block #6,841,344 Β· updates every 60s
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