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Block #30,710

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 8:19:56 PM Β· Difficulty 7.9874 Β· 6,783,363 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d8a6b47c711b0b404ef0ba73c1b29aa1c40925e70c8a586869dbe2de2e447cc1
View on Chainz β†—

Height

#30,710

Difficulty

7.987385

Transactions

1

Size

197 B

Version

2

Bits

07fcc53d

Nonce

45

Timestamp

7/13/2013, 8:19:56 PM

Confirmations

6,783,363

Merkle Root

13f4cecf9d04903832a054c84c91011ebb77ac1834130c183d3c7101769f949c
Transactions (1)
Coinbase13f4cecf9d0490…3c7101769f949c
1 in β†’ 1 out15.6500 XPM108 B
Aa6CvCkU…kRW6ZeWm
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.

2.459 Γ— 10⁹³(94-digit number)
24597814102795546147…55265717092412136620
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
2.459 Γ— 10⁹³(94-digit number)
24597814102795546147…55265717092412136619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.459 Γ— 10⁹³(94-digit number)
24597814102795546147…55265717092412136621
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
4.919 Γ— 10⁹³(94-digit number)
49195628205591092294…10531434184824273239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.919 Γ— 10⁹³(94-digit number)
49195628205591092294…10531434184824273241
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
9.839 Γ— 10⁹³(94-digit number)
98391256411182184589…21062868369648546479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.839 Γ— 10⁹³(94-digit number)
98391256411182184589…21062868369648546481
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
1.967 Γ— 10⁹⁴(95-digit number)
19678251282236436917…42125736739297092959
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 30710

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 d8a6b47c711b0b404ef0ba73c1b29aa1c40925e70c8a586869dbe2de2e447cc1

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 #30,710 on Chainz β†—
Circulating Supply:57,756,663 XPMΒ·at block #6,814,072 Β· updates every 60s
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