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Block #429,322

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2014, 5:08:45 PM Β· Difficulty 10.3461 Β· 6,365,390 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a3ccd22eb9d12920480ba078a17101929d790cbeeffabd5f85c7a5a66bc28b4e
View on Chainz β†—

Height

#429,322

Difficulty

10.346115

Transactions

1

Size

208 B

Version

2

Bits

0a589b03

Nonce

307

Timestamp

3/4/2014, 5:08:45 PM

Confirmations

6,365,390

Merkle Root

f285c99459acd41ad755c814aaddbe0c38188455c88a4c3e23d13fda696dc81e
Transactions (1)
Coinbasef285c99459acd4…d13fda696dc81e
1 in β†’ 1 out9.3300 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.

2.699 Γ— 10⁹⁸(99-digit number)
26999650154379653240…70364379766389037400
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
2.699 Γ— 10⁹⁸(99-digit number)
26999650154379653240…70364379766389037399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.699 Γ— 10⁹⁸(99-digit number)
26999650154379653240…70364379766389037401
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
5.399 Γ— 10⁹⁸(99-digit number)
53999300308759306481…40728759532778074799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.399 Γ— 10⁹⁸(99-digit number)
53999300308759306481…40728759532778074801
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
1.079 Γ— 10⁹⁹(100-digit number)
10799860061751861296…81457519065556149599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.079 Γ— 10⁹⁹(100-digit number)
10799860061751861296…81457519065556149601
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
2.159 Γ— 10⁹⁹(100-digit number)
21599720123503722592…62915038131112299199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.159 Γ— 10⁹⁹(100-digit number)
21599720123503722592…62915038131112299201
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
4.319 Γ— 10⁹⁹(100-digit number)
43199440247007445185…25830076262224598399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.319 Γ— 10⁹⁹(100-digit number)
43199440247007445185…25830076262224598401
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 429322

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 a3ccd22eb9d12920480ba078a17101929d790cbeeffabd5f85c7a5a66bc28b4e

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 #429,322 on Chainz β†—
Circulating Supply:57,601,744 XPMΒ·at block #6,794,711 Β· updates every 60s
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