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Block #341,110

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/3/2014, 6:19:08 AM Β· Difficulty 10.1316 Β· 6,455,184 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
85565001c63b09fca51d26b1bcb81d4580c1e3982fc2220587b99e6cc0afefa6
View on Chainz β†—

Height

#341,110

Difficulty

10.131585

Transactions

1

Size

205 B

Version

2

Bits

0a21af88

Nonce

170,113

Timestamp

1/3/2014, 6:19:08 AM

Confirmations

6,455,184

Merkle Root

91efbd78ef24f68d171ad62f73541618ae1aa238da022041306d74cc5b1955c3
Transactions (1)
Coinbase91efbd78ef24f6…6d74cc5b1955c3
1 in β†’ 1 out9.7300 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.

9.362 Γ— 10⁹²(93-digit number)
93623946997213488826…34058633972335150080
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
9.362 Γ— 10⁹²(93-digit number)
93623946997213488826…34058633972335150079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.362 Γ— 10⁹²(93-digit number)
93623946997213488826…34058633972335150081
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
1.872 Γ— 10⁹³(94-digit number)
18724789399442697765…68117267944670300159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.872 Γ— 10⁹³(94-digit number)
18724789399442697765…68117267944670300161
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
3.744 Γ— 10⁹³(94-digit number)
37449578798885395530…36234535889340600319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.744 Γ— 10⁹³(94-digit number)
37449578798885395530…36234535889340600321
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
7.489 Γ— 10⁹³(94-digit number)
74899157597770791061…72469071778681200639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.489 Γ— 10⁹³(94-digit number)
74899157597770791061…72469071778681200641
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
1.497 Γ— 10⁹⁴(95-digit number)
14979831519554158212…44938143557362401279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.497 Γ— 10⁹⁴(95-digit number)
14979831519554158212…44938143557362401281
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 341110

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 85565001c63b09fca51d26b1bcb81d4580c1e3982fc2220587b99e6cc0afefa6

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 #341,110 on Chainz β†—
Circulating Supply:57,614,346 XPMΒ·at block #6,796,293 Β· updates every 60s
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