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Block #349,497

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/8/2014, 11:14:36 AM Β· Difficulty 10.2741 Β· 6,482,493 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd8ae2bd66f74cd3e2bcdd85e1701dc1b5535c9330a7e03811d8a01952abc7d9
View on Chainz β†—

Height

#349,497

Difficulty

10.274056

Transactions

1

Size

206 B

Version

2

Bits

0a462889

Nonce

422,599

Timestamp

1/8/2014, 11:14:36 AM

Confirmations

6,482,493

Merkle Root

238f3d7fc6baec2459fc58837088c8085c6e8482c2ab025053e268077dacac26
Transactions (1)
Coinbase238f3d7fc6baec…e268077dacac26
1 in β†’ 1 out9.4600 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.

6.793 Γ— 10⁹⁴(95-digit number)
67932365786061724091…64345075046825472000
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
6.793 Γ— 10⁹⁴(95-digit number)
67932365786061724091…64345075046825471999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.793 Γ— 10⁹⁴(95-digit number)
67932365786061724091…64345075046825472001
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
1.358 Γ— 10⁹⁡(96-digit number)
13586473157212344818…28690150093650943999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.358 Γ— 10⁹⁡(96-digit number)
13586473157212344818…28690150093650944001
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
2.717 Γ— 10⁹⁡(96-digit number)
27172946314424689636…57380300187301887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.717 Γ— 10⁹⁡(96-digit number)
27172946314424689636…57380300187301888001
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
5.434 Γ— 10⁹⁡(96-digit number)
54345892628849379273…14760600374603775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.434 Γ— 10⁹⁡(96-digit number)
54345892628849379273…14760600374603776001
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
1.086 Γ— 10⁹⁢(97-digit number)
10869178525769875854…29521200749207551999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.086 Γ— 10⁹⁢(97-digit number)
10869178525769875854…29521200749207552001
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 349497

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 fd8ae2bd66f74cd3e2bcdd85e1701dc1b5535c9330a7e03811d8a01952abc7d9

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 #349,497 on Chainz β†—
Circulating Supply:57,900,045 XPMΒ·at block #6,831,989 Β· updates every 60s
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