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Home/Chain Registry/Block #3,003,621

Block #3,003,621

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2019, 1:32:55 PM Β· Difficulty 11.2091 Β· 3,838,234 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fee5b2d8655d9570f7577915200014f9094bc6319856324e0d401ea4259dddf4
View on Chainz β†—

Difficulty

11.209055

Transactions

1

Size

200 B

Version

2

Bits

0b3584a6

Nonce

272,764,747

Timestamp

1/10/2019, 1:32:55 PM

Confirmations

3,838,234

Merkle Root

db83a774edae834b2af8ca67559e53615f14d96447a3b3d3be89d7ec5e82a5b3
Transactions (1)
Coinbasedb83a774edae83…89d7ec5e82a5b3
1 in β†’ 1 out7.9500 XPM109 B
ASgQ5dJg…KNnQXdVe
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.

6.908 Γ— 10⁹⁡(96-digit number)
69085208604317272922…59929596925410222080
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
6.908 Γ— 10⁹⁡(96-digit number)
69085208604317272922…59929596925410222079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.908 Γ— 10⁹⁡(96-digit number)
69085208604317272922…59929596925410222081
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
1.381 Γ— 10⁹⁢(97-digit number)
13817041720863454584…19859193850820444159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.381 Γ— 10⁹⁢(97-digit number)
13817041720863454584…19859193850820444161
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
2.763 Γ— 10⁹⁢(97-digit number)
27634083441726909169…39718387701640888319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.763 Γ— 10⁹⁢(97-digit number)
27634083441726909169…39718387701640888321
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
5.526 Γ— 10⁹⁢(97-digit number)
55268166883453818338…79436775403281776639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.526 Γ— 10⁹⁢(97-digit number)
55268166883453818338…79436775403281776641
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
1.105 Γ— 10⁹⁷(98-digit number)
11053633376690763667…58873550806563553279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.105 Γ— 10⁹⁷(98-digit number)
11053633376690763667…58873550806563553281
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
2.210 Γ— 10⁹⁷(98-digit number)
22107266753381527335…17747101613127106559
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 3003621

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 fee5b2d8655d9570f7577915200014f9094bc6319856324e0d401ea4259dddf4

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 #3,003,621 on Chainz β†—
Circulating Supply:57,979,216 XPMΒ·at block #6,841,854 Β· updates every 60s
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