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Block #1,169,406

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/25/2015, 6:59:25 AM · Difficulty 10.9353 · 5,674,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2413411e22eafff61c5ed1facfb9c1e511e51b7782bce7050cc8108bedd1133d

View on Chainz ↗

Height

#1,169,406

Difficulty

10.935337

Transactions

Size

653 B

Version

Bits

0aef7240

Nonce

1,448,179,758

Timestamp

7/25/2015, 6:59:25 AM

Confirmations

5,674,360

Merkle Root

bc3695b0c395da6b3f6969d319f83a175c238422d9da6650ee0ae27dd20f83b2

Transactions (3)

Coinbase93d77bf715d174…7fe9006f006bbb

1 in → 1 out8.3700 XPM110 B

AGnSsMxD…zXuM75m5

3a36dcce78a254…b38be28e7229df

1 in → 2 out99333.3881 XPM225 B

AScodGer…kaTbUTzb AQBu97Mx…59S1DMVx

a35c61c608178a…4c5567e7f541ad

1 in → 2 out21459.6265 XPM226 B

Aa1thDF7…ZhBM8toj AScodGer…kaTbUTzb

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.147 × 10⁹⁸(99-digit number)

41475820468164705617…43601264273936875520

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

4.147 × 10⁹⁸(99-digit number)

41475820468164705617…43601264273936875519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.147 × 10⁹⁸(99-digit number)

41475820468164705617…43601264273936875521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

8.295 × 10⁹⁸(99-digit number)

82951640936329411234…87202528547873751039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.295 × 10⁹⁸(99-digit number)

82951640936329411234…87202528547873751041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.659 × 10⁹⁹(100-digit number)

16590328187265882246…74405057095747502079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.659 × 10⁹⁹(100-digit number)

16590328187265882246…74405057095747502081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.318 × 10⁹⁹(100-digit number)

33180656374531764493…48810114191495004159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.318 × 10⁹⁹(100-digit number)

33180656374531764493…48810114191495004161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.636 × 10⁹⁹(100-digit number)

66361312749063528987…97620228382990008319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.636 × 10⁹⁹(100-digit number)

66361312749063528987…97620228382990008321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — 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 →

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 1169406

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 2413411e22eafff61c5ed1facfb9c1e511e51b7782bce7050cc8108bedd1133d

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 → Debug Window → 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 #1,169,406 on Chainz ↗

Block #1,169,406

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