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Home/Chain Registry/Block #2,634,105

Block #2,634,105

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 6:34:23 PM Β· Difficulty 11.2227 Β· 4,207,826 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ee0e80ddbfacac0ec240ff7e3685bdc93d4c4682945d8888b9820c22ed1ea45c
View on Chainz β†—

Difficulty

11.222665

Transactions

1

Size

200 B

Version

2

Bits

0b390099

Nonce

272,551,464

Timestamp

4/28/2018, 6:34:23 PM

Confirmations

4,207,826

Merkle Root

bb559e0fb147d638e8fa5be83b71cfa498bfce6ec3c6317eb9eeeaca1b8af512
Transactions (1)
Coinbasebb559e0fb147d6…eeeaca1b8af512
1 in β†’ 1 out7.9300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.104 Γ— 10⁹⁡(96-digit number)
31041210103449274076…51373013954027882880
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
3.104 Γ— 10⁹⁡(96-digit number)
31041210103449274076…51373013954027882879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.104 Γ— 10⁹⁡(96-digit number)
31041210103449274076…51373013954027882881
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
6.208 Γ— 10⁹⁡(96-digit number)
62082420206898548152…02746027908055765759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.208 Γ— 10⁹⁡(96-digit number)
62082420206898548152…02746027908055765761
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
1.241 Γ— 10⁹⁢(97-digit number)
12416484041379709630…05492055816111531519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.241 Γ— 10⁹⁢(97-digit number)
12416484041379709630…05492055816111531521
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
2.483 Γ— 10⁹⁢(97-digit number)
24832968082759419261…10984111632223063039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.483 Γ— 10⁹⁢(97-digit number)
24832968082759419261…10984111632223063041
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
4.966 Γ— 10⁹⁢(97-digit number)
49665936165518838522…21968223264446126079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.966 Γ— 10⁹⁢(97-digit number)
49665936165518838522…21968223264446126081
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
9.933 Γ— 10⁹⁢(97-digit number)
99331872331037677044…43936446528892252159
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 2634105

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 ee0e80ddbfacac0ec240ff7e3685bdc93d4c4682945d8888b9820c22ed1ea45c

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 #2,634,105 on Chainz β†—
Circulating Supply:57,979,826 XPMΒ·at block #6,841,930 Β· updates every 60s
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