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Block #425,492

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/1/2014, 11:19:24 PM Β· Difficulty 10.3587 Β· 6,412,796 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3fa9e3a52474a78fa87fb3983b27842399f5cd663d5a7e6874fb6c9c722c3a50
View on Chainz β†—

Height

#425,492

Difficulty

10.358683

Transactions

2

Size

425 B

Version

2

Bits

0a5bd2a4

Nonce

1,761,319

Timestamp

3/1/2014, 11:19:24 PM

Confirmations

6,412,796

Merkle Root

ba6155e59488b764bfcd5d2b0a27c599a6c9dea32c550f7c9d81e50e510e3e37
Transactions (2)
Coinbaseb6377abc8fb07d…31cf67c160d092
1 in β†’ 1 out9.3200 XPM109 B
AW2mLi9j…d5eatduS
d1dc9cb9941749…48a95b783e4972
1 in β†’ 2 out4.1349 XPM225 B
Aa1qENW3…TQGufWxrARd47WCo…vXzjgLiX
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.

1.291 Γ— 10⁹⁢(97-digit number)
12915453816318204030…92092447488789171200
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
1.291 Γ— 10⁹⁢(97-digit number)
12915453816318204030…92092447488789171199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.291 Γ— 10⁹⁢(97-digit number)
12915453816318204030…92092447488789171201
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
2.583 Γ— 10⁹⁢(97-digit number)
25830907632636408061…84184894977578342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.583 Γ— 10⁹⁢(97-digit number)
25830907632636408061…84184894977578342401
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
5.166 Γ— 10⁹⁢(97-digit number)
51661815265272816122…68369789955156684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.166 Γ— 10⁹⁢(97-digit number)
51661815265272816122…68369789955156684801
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
1.033 Γ— 10⁹⁷(98-digit number)
10332363053054563224…36739579910313369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.033 Γ— 10⁹⁷(98-digit number)
10332363053054563224…36739579910313369601
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
2.066 Γ— 10⁹⁷(98-digit number)
20664726106109126449…73479159820626739199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.066 Γ— 10⁹⁷(98-digit number)
20664726106109126449…73479159820626739201
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 425492

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 3fa9e3a52474a78fa87fb3983b27842399f5cd663d5a7e6874fb6c9c722c3a50

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 #425,492 on Chainz β†—
Circulating Supply:57,950,585 XPMΒ·at block #6,838,287 Β· updates every 60s
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