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Block #321,864

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2013, 2:06:55 PM Β· Difficulty 10.1990 Β· 6,489,917 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe718adb419efd181b857383989ddbeb8a13d1a1f9b3e3cca24637ee04b40a8b
View on Chainz β†—

Height

#321,864

Difficulty

10.199048

Transactions

1

Size

205 B

Version

2

Bits

0a32f4c9

Nonce

89,873

Timestamp

12/20/2013, 2:06:55 PM

Confirmations

6,489,917

Merkle Root

97a3dd6d4e0b50e011c5271c3ec5aada750ad9908f5e9a06344447c05dadbd19
Transactions (1)
Coinbase97a3dd6d4e0b50…4447c05dadbd19
1 in β†’ 1 out9.6000 XPM116 B
AbwWkWZt…kawDhufa
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.

2.343 Γ— 10⁹³(94-digit number)
23434998900295239204…91708227601814092800
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
2.343 Γ— 10⁹³(94-digit number)
23434998900295239204…91708227601814092799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.343 Γ— 10⁹³(94-digit number)
23434998900295239204…91708227601814092801
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
4.686 Γ— 10⁹³(94-digit number)
46869997800590478409…83416455203628185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.686 Γ— 10⁹³(94-digit number)
46869997800590478409…83416455203628185601
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
9.373 Γ— 10⁹³(94-digit number)
93739995601180956818…66832910407256371199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.373 Γ— 10⁹³(94-digit number)
93739995601180956818…66832910407256371201
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
1.874 Γ— 10⁹⁴(95-digit number)
18747999120236191363…33665820814512742399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.874 Γ— 10⁹⁴(95-digit number)
18747999120236191363…33665820814512742401
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
3.749 Γ— 10⁹⁴(95-digit number)
37495998240472382727…67331641629025484799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.749 Γ— 10⁹⁴(95-digit number)
37495998240472382727…67331641629025484801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 321864

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 fe718adb419efd181b857383989ddbeb8a13d1a1f9b3e3cca24637ee04b40a8b

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 #321,864 on Chainz β†—
Circulating Supply:57,738,360 XPMΒ·at block #6,811,780 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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