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Block #33,752

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 5:25:50 AM Β· Difficulty 7.9924 Β· 6,784,072 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6af7adacc181358de354a4c2011262b070b3ae838351d443590160ffe2c7334d
View on Chainz β†—

Height

#33,752

Difficulty

7.992382

Transactions

1

Size

198 B

Version

2

Bits

07fe0cc5

Nonce

356

Timestamp

7/14/2013, 5:25:50 AM

Confirmations

6,784,072

Merkle Root

7a45c21d2b378c887aa71ab7493394fcf8c91c29f11e8fa7fb9041fca697a3db
Transactions (1)
Coinbase7a45c21d2b378c…9041fca697a3db
1 in β†’ 1 out15.6300 XPM109 B
ASbRxSSz…H5rkdjdH
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.

6.732 Γ— 10⁹²(93-digit number)
67321206636783034523…05265856462260417320
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
6.732 Γ— 10⁹²(93-digit number)
67321206636783034523…05265856462260417319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.732 Γ— 10⁹²(93-digit number)
67321206636783034523…05265856462260417321
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
1.346 Γ— 10⁹³(94-digit number)
13464241327356606904…10531712924520834639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.346 Γ— 10⁹³(94-digit number)
13464241327356606904…10531712924520834641
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
2.692 Γ— 10⁹³(94-digit number)
26928482654713213809…21063425849041669279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.692 Γ— 10⁹³(94-digit number)
26928482654713213809…21063425849041669281
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
5.385 Γ— 10⁹³(94-digit number)
53856965309426427618…42126851698083338559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.385 Γ— 10⁹³(94-digit number)
53856965309426427618…42126851698083338561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 33752

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 6af7adacc181358de354a4c2011262b070b3ae838351d443590160ffe2c7334d

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 #33,752 on Chainz β†—
Circulating Supply:57,786,656 XPMΒ·at block #6,817,823 Β· updates every 60s
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