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Block #134,685

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2013, 4:40:42 AM Β· Difficulty 9.8061 Β· 6,691,022 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3c3bf590ee3086b05db3debd0e309134854ef88215e87e625b8054c78f1ff6b6
View on Chainz β†—

Height

#134,685

Difficulty

9.806114

Transactions

1

Size

199 B

Version

2

Bits

09ce5d7d

Nonce

595,761

Timestamp

8/26/2013, 4:40:42 AM

Confirmations

6,691,022

Merkle Root

3a932d8e266b1de96bfabc944a9a8d96c7c877b7c5f3a1906496c76a6bf1ca8c
Transactions (1)
Coinbase3a932d8e266b1d…96c76a6bf1ca8c
1 in β†’ 1 out10.3800 XPM109 B
AV55pf9g…c4Jbvptx
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.

2.285 Γ— 10⁹⁴(95-digit number)
22857346426807759334…31505027586640933700
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
2.285 Γ— 10⁹⁴(95-digit number)
22857346426807759334…31505027586640933699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.285 Γ— 10⁹⁴(95-digit number)
22857346426807759334…31505027586640933701
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
4.571 Γ— 10⁹⁴(95-digit number)
45714692853615518669…63010055173281867399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.571 Γ— 10⁹⁴(95-digit number)
45714692853615518669…63010055173281867401
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
9.142 Γ— 10⁹⁴(95-digit number)
91429385707231037338…26020110346563734799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.142 Γ— 10⁹⁴(95-digit number)
91429385707231037338…26020110346563734801
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
1.828 Γ— 10⁹⁡(96-digit number)
18285877141446207467…52040220693127469599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.828 Γ— 10⁹⁡(96-digit number)
18285877141446207467…52040220693127469601
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
3.657 Γ— 10⁹⁡(96-digit number)
36571754282892414935…04080441386254939199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 134685

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 3c3bf590ee3086b05db3debd0e309134854ef88215e87e625b8054c78f1ff6b6

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 #134,685 on Chainz β†—
Circulating Supply:57,849,760 XPMΒ·at block #6,825,706 Β· updates every 60s
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