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Home/Chain Registry/Block #1,236,346

Block #1,236,346

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2015, 12:03:18 PM Β· Difficulty 10.7544 Β· 5,564,071 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ed97d0a07a6a2aedcb38c2270811155fb834ac554108ae1b5b6ba294ce89cd1
View on Chainz β†—

Difficulty

10.754440

Transactions

1

Size

197 B

Version

2

Bits

0ac12302

Nonce

410,658,631

Timestamp

9/14/2015, 12:03:18 PM

Confirmations

5,564,071

Merkle Root

0ff684ef3d28450b7767e4c2ca0e797d25d77143724d21a547333c2ed4eac059
Transactions (1)
Coinbase0ff684ef3d2845…333c2ed4eac059
1 in β†’ 1 out8.6300 XPM109 B
AHdJQKjG…g9kBd7Qi
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.

2.133 Γ— 10⁸⁹(90-digit number)
21336604124446658136…76659789599515478400
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
2.133 Γ— 10⁸⁹(90-digit number)
21336604124446658136…76659789599515478399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.133 Γ— 10⁸⁹(90-digit number)
21336604124446658136…76659789599515478401
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
4.267 Γ— 10⁸⁹(90-digit number)
42673208248893316272…53319579199030956799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.267 Γ— 10⁸⁹(90-digit number)
42673208248893316272…53319579199030956801
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
8.534 Γ— 10⁸⁹(90-digit number)
85346416497786632544…06639158398061913599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.534 Γ— 10⁸⁹(90-digit number)
85346416497786632544…06639158398061913601
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
1.706 Γ— 10⁹⁰(91-digit number)
17069283299557326508…13278316796123827199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.706 Γ— 10⁹⁰(91-digit number)
17069283299557326508…13278316796123827201
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
3.413 Γ— 10⁹⁰(91-digit number)
34138566599114653017…26556633592247654399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.413 Γ— 10⁹⁰(91-digit number)
34138566599114653017…26556633592247654401
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 1236346

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 1ed97d0a07a6a2aedcb38c2270811155fb834ac554108ae1b5b6ba294ce89cd1

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 #1,236,346 on Chainz β†—
Circulating Supply:57,647,400 XPMΒ·at block #6,800,416 Β· updates every 60s
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