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Home/Chain Registry/Block #2,623,281

Block #2,623,281

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/21/2018, 6:30:40 AM Β· Difficulty 11.2193 Β· 4,213,477 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bab19359429bf6f196581ab30faa9f2a7f3b4f1e383a35aea3c72d87d1f9ed7c
View on Chainz β†—

Difficulty

11.219258

Transactions

1

Size

199 B

Version

2

Bits

0b382143

Nonce

1,529,654,068

Timestamp

4/21/2018, 6:30:40 AM

Confirmations

4,213,477

Merkle Root

d38284b504a27f52c7ac62d8f28528ebbd1253ddfdeed6c989829c309f8c1c0d
Transactions (1)
Coinbased38284b504a27f…829c309f8c1c0d
1 in β†’ 1 out7.9300 XPM109 B
AT9gytRP…fhtGYm6h
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.

3.442 Γ— 10⁹⁡(96-digit number)
34425587512480505297…67821808665414443520
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
3.442 Γ— 10⁹⁡(96-digit number)
34425587512480505297…67821808665414443519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.442 Γ— 10⁹⁡(96-digit number)
34425587512480505297…67821808665414443521
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
6.885 Γ— 10⁹⁡(96-digit number)
68851175024961010594…35643617330828887039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.885 Γ— 10⁹⁡(96-digit number)
68851175024961010594…35643617330828887041
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
1.377 Γ— 10⁹⁢(97-digit number)
13770235004992202118…71287234661657774079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.377 Γ— 10⁹⁢(97-digit number)
13770235004992202118…71287234661657774081
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
2.754 Γ— 10⁹⁢(97-digit number)
27540470009984404237…42574469323315548159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.754 Γ— 10⁹⁢(97-digit number)
27540470009984404237…42574469323315548161
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
5.508 Γ— 10⁹⁢(97-digit number)
55080940019968808475…85148938646631096319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.508 Γ— 10⁹⁢(97-digit number)
55080940019968808475…85148938646631096321
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
1.101 Γ— 10⁹⁷(98-digit number)
11016188003993761695…70297877293262192639
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 2623281

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 bab19359429bf6f196581ab30faa9f2a7f3b4f1e383a35aea3c72d87d1f9ed7c

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 #2,623,281 on Chainz β†—
Circulating Supply:57,938,346 XPMΒ·at block #6,836,757 Β· updates every 60s
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