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Home/Chain Registry/Block #2,932,201

Block #2,932,201

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2018, 11:34:17 PM Β· Difficulty 11.4004 Β· 3,900,686 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2ea0a74f8644d38cf2f7de6a12dfa337b8600ed06a1f1c184560d92616e7e0a2
View on Chainz β†—

Difficulty

11.400424

Transactions

1

Size

201 B

Version

2

Bits

0b668237

Nonce

1,110,998,408

Timestamp

11/20/2018, 11:34:17 PM

Confirmations

3,900,686

Merkle Root

c91e1d4f51bd48bf05552f72ffa170386edd7174a89a7d7dc70010523274eda9
Transactions (1)
Coinbasec91e1d4f51bd48…0010523274eda9
1 in β†’ 1 out7.6800 XPM110 B
AbXwmGxD…4XXYP765
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.

1.367 Γ— 10⁹⁢(97-digit number)
13671866875971297038…84829600825927039040
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
1.367 Γ— 10⁹⁢(97-digit number)
13671866875971297038…84829600825927039039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.367 Γ— 10⁹⁢(97-digit number)
13671866875971297038…84829600825927039041
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
2.734 Γ— 10⁹⁢(97-digit number)
27343733751942594077…69659201651854078079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.734 Γ— 10⁹⁢(97-digit number)
27343733751942594077…69659201651854078081
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
5.468 Γ— 10⁹⁢(97-digit number)
54687467503885188155…39318403303708156159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.468 Γ— 10⁹⁢(97-digit number)
54687467503885188155…39318403303708156161
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
1.093 Γ— 10⁹⁷(98-digit number)
10937493500777037631…78636806607416312319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.093 Γ— 10⁹⁷(98-digit number)
10937493500777037631…78636806607416312321
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
2.187 Γ— 10⁹⁷(98-digit number)
21874987001554075262…57273613214832624639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.187 Γ— 10⁹⁷(98-digit number)
21874987001554075262…57273613214832624641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.374 Γ— 10⁹⁷(98-digit number)
43749974003108150524…14547226429665249279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2932201

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 2ea0a74f8644d38cf2f7de6a12dfa337b8600ed06a1f1c184560d92616e7e0a2

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 #2,932,201 on Chainz β†—
Circulating Supply:57,907,265 XPMΒ·at block #6,832,886 Β· updates every 60s
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