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Block #33,487

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 4:57:16 AM Β· Difficulty 7.9920 Β· 6,784,207 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
851ca5372372f8c178494efdc8bb348093e66281c9ce48fac4a0c93a783c43cd
View on Chainz β†—

Height

#33,487

Difficulty

7.992008

Transactions

1

Size

198 B

Version

2

Bits

07fdf43b

Nonce

594

Timestamp

7/14/2013, 4:57:16 AM

Confirmations

6,784,207

Merkle Root

d12e18233da7516fe5863194907e637183c6ca8906660d283f50ce904ce7c807
Transactions (1)
Coinbased12e18233da751…50ce904ce7c807
1 in β†’ 1 out15.6400 XPM109 B
ALXjrugC…hByoynjy
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.

2.112 Γ— 10⁹³(94-digit number)
21126384452413573641…13958814214478071800
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
2.112 Γ— 10⁹³(94-digit number)
21126384452413573641…13958814214478071799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.112 Γ— 10⁹³(94-digit number)
21126384452413573641…13958814214478071801
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
4.225 Γ— 10⁹³(94-digit number)
42252768904827147282…27917628428956143599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.225 Γ— 10⁹³(94-digit number)
42252768904827147282…27917628428956143601
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
8.450 Γ— 10⁹³(94-digit number)
84505537809654294565…55835256857912287199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.450 Γ— 10⁹³(94-digit number)
84505537809654294565…55835256857912287201
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
1.690 Γ— 10⁹⁴(95-digit number)
16901107561930858913…11670513715824574399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 33487

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 851ca5372372f8c178494efdc8bb348093e66281c9ce48fac4a0c93a783c43cd

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 #33,487 on Chainz β†—
Circulating Supply:57,785,610 XPMΒ·at block #6,817,693 Β· updates every 60s
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