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Block #329,086

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/25/2013, 5:33:39 PM Β· Difficulty 10.1709 Β· 6,483,768 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1d0c2d9bc020e1a76c29a807a53ebd0074fb37c75bfec55359a217b9c2464932
View on Chainz β†—

Height

#329,086

Difficulty

10.170860

Transactions

1

Size

969 B

Version

2

Bits

0a2bbd7c

Nonce

14,090

Timestamp

12/25/2013, 5:33:39 PM

Confirmations

6,483,768

Merkle Root

2fedac2e13643857218a14a8926a389a3eeb61d6eef8d04034ae0a19156351e3
Transactions (1)
Coinbase2fedac2e136438…ae0a19156351e3
1 in β†’ 24 out9.6500 XPM879 B
ANvouN5N…Cbayu95bAQwRN8bE…V8PsTcY9AK6M6ovi…8x1avD8eAac9Hjdg…P4ktypc3AQ8QAT3J…rCFKuVbR
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.

6.869 Γ— 10⁹³(94-digit number)
68698318702257114422…21078147888753607480
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
6.869 Γ— 10⁹³(94-digit number)
68698318702257114422…21078147888753607479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.869 Γ— 10⁹³(94-digit number)
68698318702257114422…21078147888753607481
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
1.373 Γ— 10⁹⁴(95-digit number)
13739663740451422884…42156295777507214959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.373 Γ— 10⁹⁴(95-digit number)
13739663740451422884…42156295777507214961
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
2.747 Γ— 10⁹⁴(95-digit number)
27479327480902845768…84312591555014429919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.747 Γ— 10⁹⁴(95-digit number)
27479327480902845768…84312591555014429921
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
5.495 Γ— 10⁹⁴(95-digit number)
54958654961805691537…68625183110028859839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.495 Γ— 10⁹⁴(95-digit number)
54958654961805691537…68625183110028859841
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
1.099 Γ— 10⁹⁡(96-digit number)
10991730992361138307…37250366220057719679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.099 Γ— 10⁹⁡(96-digit number)
10991730992361138307…37250366220057719681
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 329086

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 1d0c2d9bc020e1a76c29a807a53ebd0074fb37c75bfec55359a217b9c2464932

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 #329,086 on Chainz β†—
Circulating Supply:57,746,868 XPMΒ·at block #6,812,853 Β· updates every 60s
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