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Home/Chain Registry/Block #1,798,507

Block #1,798,507

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/8/2016, 8:58:30 PM Β· Difficulty 10.7758 Β· 5,019,404 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a4e3cbd15ab35b4da229f5596c2c2aa04ae8e783314e93bf9c6bcff30484d16
View on Chainz β†—

Difficulty

10.775771

Transactions

1

Size

200 B

Version

2

Bits

0ac698e9

Nonce

1,921,604,296

Timestamp

10/8/2016, 8:58:30 PM

Confirmations

5,019,404

Merkle Root

2b0763f2320cf42f647df6ce93fcf8da58041cf661c13ca9b052b2c76c12f083
Transactions (1)
Coinbase2b0763f2320cf4…52b2c76c12f083
1 in β†’ 1 out8.6000 XPM110 B
AJnmsEaw…dWfHRdAJ
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.

3.513 Γ— 10⁹³(94-digit number)
35132351968002411555…10372440434659198080
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
3.513 Γ— 10⁹³(94-digit number)
35132351968002411555…10372440434659198079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.513 Γ— 10⁹³(94-digit number)
35132351968002411555…10372440434659198081
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
7.026 Γ— 10⁹³(94-digit number)
70264703936004823110…20744880869318396159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.026 Γ— 10⁹³(94-digit number)
70264703936004823110…20744880869318396161
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
1.405 Γ— 10⁹⁴(95-digit number)
14052940787200964622…41489761738636792319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.405 Γ— 10⁹⁴(95-digit number)
14052940787200964622…41489761738636792321
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
2.810 Γ— 10⁹⁴(95-digit number)
28105881574401929244…82979523477273584639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.810 Γ— 10⁹⁴(95-digit number)
28105881574401929244…82979523477273584641
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
5.621 Γ— 10⁹⁴(95-digit number)
56211763148803858488…65959046954547169279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.621 Γ— 10⁹⁴(95-digit number)
56211763148803858488…65959046954547169281
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
1.124 Γ— 10⁹⁡(96-digit number)
11242352629760771697…31918093909094338559
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 1798507

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 9a4e3cbd15ab35b4da229f5596c2c2aa04ae8e783314e93bf9c6bcff30484d16

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 #1,798,507 on Chainz β†—
Circulating Supply:57,787,352 XPMΒ·at block #6,817,910 Β· updates every 60s
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