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Home/Chain Registry/Block #2,088,398

Block #2,088,398

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2017, 7:43:39 AM Β· Difficulty 10.8754 Β· 4,745,378 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58f1129fa866f7be525de990354c4b275b44efc2e8cbaa57bd1ff4b66e6e6fdb
View on Chainz β†—

Difficulty

10.875406

Transactions

1

Size

200 B

Version

2

Bits

0ae01a9c

Nonce

950,319,221

Timestamp

4/26/2017, 7:43:39 AM

Confirmations

4,745,378

Merkle Root

f2d58ebbf3e41d2c51bc0b628a0495e3646e2f4491795ffe90f902be03f6dd75
Transactions (1)
Coinbasef2d58ebbf3e41d…f902be03f6dd75
1 in β†’ 1 out8.4400 XPM109 B
AMATs6di…eGepsgR7
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.

6.695 Γ— 10⁹⁢(97-digit number)
66956331473167841331…94537830817712742400
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
6.695 Γ— 10⁹⁢(97-digit number)
66956331473167841331…94537830817712742399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.695 Γ— 10⁹⁢(97-digit number)
66956331473167841331…94537830817712742401
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
1.339 Γ— 10⁹⁷(98-digit number)
13391266294633568266…89075661635425484799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.339 Γ— 10⁹⁷(98-digit number)
13391266294633568266…89075661635425484801
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
2.678 Γ— 10⁹⁷(98-digit number)
26782532589267136532…78151323270850969599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.678 Γ— 10⁹⁷(98-digit number)
26782532589267136532…78151323270850969601
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
5.356 Γ— 10⁹⁷(98-digit number)
53565065178534273065…56302646541701939199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.356 Γ— 10⁹⁷(98-digit number)
53565065178534273065…56302646541701939201
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
1.071 Γ— 10⁹⁸(99-digit number)
10713013035706854613…12605293083403878399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.071 Γ— 10⁹⁸(99-digit number)
10713013035706854613…12605293083403878401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2088398

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 58f1129fa866f7be525de990354c4b275b44efc2e8cbaa57bd1ff4b66e6e6fdb

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 #2,088,398 on Chainz β†—
Circulating Supply:57,914,426 XPMΒ·at block #6,833,775 Β· updates every 60s
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