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Block #235,935

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/31/2013, 5:32:42 AM Β· Difficulty 9.9463 Β· 6,595,915 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4cbbb11cb48f85bdf1e378ba75d7527300fcdf2a30658542497ff52ad64c9d0b
View on Chainz β†—

Height

#235,935

Difficulty

9.946324

Transactions

1

Size

208 B

Version

2

Bits

09f24243

Nonce

310,491

Timestamp

10/31/2013, 5:32:42 AM

Confirmations

6,595,915

Merkle Root

5a50c09e6886ef2121663d2a26c2bf896dbed8ae375e6fda9de9ad3fc0757545
Transactions (1)
Coinbase5a50c09e6886ef…e9ad3fc0757545
1 in β†’ 1 out10.0900 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.461 Γ— 10¹⁰⁰(101-digit number)
34610332952383936728…81672099669658624000
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
3.461 Γ— 10¹⁰⁰(101-digit number)
34610332952383936728…81672099669658623999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.461 Γ— 10¹⁰⁰(101-digit number)
34610332952383936728…81672099669658624001
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
6.922 Γ— 10¹⁰⁰(101-digit number)
69220665904767873457…63344199339317247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.922 Γ— 10¹⁰⁰(101-digit number)
69220665904767873457…63344199339317248001
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
1.384 Γ— 10¹⁰¹(102-digit number)
13844133180953574691…26688398678634495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.384 Γ— 10¹⁰¹(102-digit number)
13844133180953574691…26688398678634496001
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
2.768 Γ— 10¹⁰¹(102-digit number)
27688266361907149382…53376797357268991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.768 Γ— 10¹⁰¹(102-digit number)
27688266361907149382…53376797357268992001
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
5.537 Γ— 10¹⁰¹(102-digit number)
55376532723814298765…06753594714537983999
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 235935

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 4cbbb11cb48f85bdf1e378ba75d7527300fcdf2a30658542497ff52ad64c9d0b

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 #235,935 on Chainz β†—
Circulating Supply:57,898,922 XPMΒ·at block #6,831,849 Β· updates every 60s
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