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Home/Chain Registry/Block #2,133,336

Block #2,133,336

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 10:44:53 AM Β· Difficulty 10.9097 Β· 4,707,365 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
24b9e813443e6fe4517b955fc4c47ae901ab7cb834535ae2ca3653c952d7d996
View on Chainz β†—

Difficulty

10.909747

Transactions

1

Size

200 B

Version

2

Bits

0ae8e52a

Nonce

1,164,302,449

Timestamp

5/26/2017, 10:44:53 AM

Confirmations

4,707,365

Merkle Root

1aa2dcfba892720643c2fc0e0766ad3034dc45efe782fea74329b63c4ca82d0b
Transactions (1)
Coinbase1aa2dcfba89272…29b63c4ca82d0b
1 in β†’ 1 out8.3900 XPM109 B
AKSiPj9X…1SgHtZPG
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.

1.716 Γ— 10⁹⁷(98-digit number)
17165493362064470822…45078648893301248000
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
1.716 Γ— 10⁹⁷(98-digit number)
17165493362064470822…45078648893301247999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.716 Γ— 10⁹⁷(98-digit number)
17165493362064470822…45078648893301248001
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
3.433 Γ— 10⁹⁷(98-digit number)
34330986724128941645…90157297786602495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.433 Γ— 10⁹⁷(98-digit number)
34330986724128941645…90157297786602496001
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
6.866 Γ— 10⁹⁷(98-digit number)
68661973448257883291…80314595573204991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.866 Γ— 10⁹⁷(98-digit number)
68661973448257883291…80314595573204992001
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
1.373 Γ— 10⁹⁸(99-digit number)
13732394689651576658…60629191146409983999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.373 Γ— 10⁹⁸(99-digit number)
13732394689651576658…60629191146409984001
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
2.746 Γ— 10⁹⁸(99-digit number)
27464789379303153316…21258382292819967999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.746 Γ— 10⁹⁸(99-digit number)
27464789379303153316…21258382292819968001
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
5.492 Γ— 10⁹⁸(99-digit number)
54929578758606306633…42516764585639935999
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 2133336

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 24b9e813443e6fe4517b955fc4c47ae901ab7cb834535ae2ca3653c952d7d996

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 #2,133,336 on Chainz β†—
Circulating Supply:57,969,949 XPMΒ·at block #6,840,700 Β· updates every 60s
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