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Block #31,487

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 11:35:38 PM Β· Difficulty 7.9888 Β· 6,782,356 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8efc5ae1da32074f97223987442028ed05894eae1003de788317f730e23b51f3
View on Chainz β†—

Height

#31,487

Difficulty

7.988780

Transactions

1

Size

198 B

Version

2

Bits

07fd20b3

Nonce

31

Timestamp

7/13/2013, 11:35:38 PM

Confirmations

6,782,356

Merkle Root

e3c52a917b9db1294edd6e6d56b23ab3fe22472b87f761a8062959078d0a5ca6
Transactions (1)
Coinbasee3c52a917b9db1…2959078d0a5ca6
1 in β†’ 1 out15.6500 XPM108 B
AG4TgV8u…QvpXGs8i
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.

7.178 Γ— 10⁹⁴(95-digit number)
71785723409951932275…34239534148380206400
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
7.178 Γ— 10⁹⁴(95-digit number)
71785723409951932275…34239534148380206399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.178 Γ— 10⁹⁴(95-digit number)
71785723409951932275…34239534148380206401
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
1.435 Γ— 10⁹⁡(96-digit number)
14357144681990386455…68479068296760412799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.435 Γ— 10⁹⁡(96-digit number)
14357144681990386455…68479068296760412801
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
2.871 Γ— 10⁹⁡(96-digit number)
28714289363980772910…36958136593520825599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.871 Γ— 10⁹⁡(96-digit number)
28714289363980772910…36958136593520825601
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
5.742 Γ— 10⁹⁡(96-digit number)
57428578727961545820…73916273187041651199
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 31487

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 8efc5ae1da32074f97223987442028ed05894eae1003de788317f730e23b51f3

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 #31,487 on Chainz β†—
Circulating Supply:57,754,813 XPMΒ·at block #6,813,842 Β· updates every 60s
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