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Block #453,191

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/21/2014, 2:33:16 AM Β· Difficulty 10.3929 Β· 6,385,933 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffbfb9c40f2b37d18a070f230818ba9e1fd905e0932fa0932c4c6002280f2c3f
View on Chainz β†—

Height

#453,191

Difficulty

10.392948

Transactions

1

Size

200 B

Version

2

Bits

0a649837

Nonce

435,556

Timestamp

3/21/2014, 2:33:16 AM

Confirmations

6,385,933

Merkle Root

1eacd9bd638681cebf198142c1a401bf44bc15a04c02db7f64e1b4c26605b5aa
Transactions (1)
Coinbase1eacd9bd638681…e1b4c26605b5aa
1 in β†’ 1 out9.2400 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.966 Γ— 10⁹³(94-digit number)
29664539102480581282…14167571959179674240
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
2.966 Γ— 10⁹³(94-digit number)
29664539102480581282…14167571959179674239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.966 Γ— 10⁹³(94-digit number)
29664539102480581282…14167571959179674241
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
5.932 Γ— 10⁹³(94-digit number)
59329078204961162564…28335143918359348479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.932 Γ— 10⁹³(94-digit number)
59329078204961162564…28335143918359348481
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
1.186 Γ— 10⁹⁴(95-digit number)
11865815640992232512…56670287836718696959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.186 Γ— 10⁹⁴(95-digit number)
11865815640992232512…56670287836718696961
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
2.373 Γ— 10⁹⁴(95-digit number)
23731631281984465025…13340575673437393919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.373 Γ— 10⁹⁴(95-digit number)
23731631281984465025…13340575673437393921
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
4.746 Γ— 10⁹⁴(95-digit number)
47463262563968930051…26681151346874787839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.746 Γ— 10⁹⁴(95-digit number)
47463262563968930051…26681151346874787841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.492 Γ— 10⁹⁴(95-digit number)
94926525127937860102…53362302693749575679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 453191

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 ffbfb9c40f2b37d18a070f230818ba9e1fd905e0932fa0932c4c6002280f2c3f

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 #453,191 on Chainz β†—
Circulating Supply:57,957,268 XPMΒ·at block #6,839,123 Β· updates every 60s
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