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Home/Chain Registry/Block #2,131,992

Block #2,131,992

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/25/2017, 11:49:32 AM Β· Difficulty 10.9103 Β· 4,712,152 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1b28c8ad334665d216c00808ae67f416bdfde2e9e4e245133327cce4e9e85926
View on Chainz β†—

Difficulty

10.910282

Transactions

1

Size

200 B

Version

2

Bits

0ae9083a

Nonce

1,197,219,953

Timestamp

5/25/2017, 11:49:32 AM

Confirmations

4,712,152

Merkle Root

aea64e7d5867ca3be17e50d92f0d5c64c36f9983bc6ab0bf94ff2f5521b951da
Transactions (1)
Coinbaseaea64e7d5867ca…ff2f5521b951da
1 in β†’ 1 out8.3900 XPM109 B
AWGTTP6Y…wwjhjBo7
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.

1.338 Γ— 10⁹⁷(98-digit number)
13387480048175290633…26193383164033751040
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
1.338 Γ— 10⁹⁷(98-digit number)
13387480048175290633…26193383164033751039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13387480048175290633…26193383164033751041
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
2.677 Γ— 10⁹⁷(98-digit number)
26774960096350581266…52386766328067502079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.677 Γ— 10⁹⁷(98-digit number)
26774960096350581266…52386766328067502081
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
5.354 Γ— 10⁹⁷(98-digit number)
53549920192701162533…04773532656135004159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.354 Γ— 10⁹⁷(98-digit number)
53549920192701162533…04773532656135004161
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
1.070 Γ— 10⁹⁸(99-digit number)
10709984038540232506…09547065312270008319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.070 Γ— 10⁹⁸(99-digit number)
10709984038540232506…09547065312270008321
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
2.141 Γ— 10⁹⁸(99-digit number)
21419968077080465013…19094130624540016639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.141 Γ— 10⁹⁸(99-digit number)
21419968077080465013…19094130624540016641
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 2131992

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 1b28c8ad334665d216c00808ae67f416bdfde2e9e4e245133327cce4e9e85926

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 #2,131,992 on Chainz β†—
Circulating Supply:57,997,528 XPMΒ·at block #6,844,143 Β· updates every 60s
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