Home/Chain Registry/Block #127,529

Block #127,529

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/21/2013, 2:24:25 PM · Difficulty 9.7838 · 6,688,846 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a6ede52ff0a8aab41384159cceedbb680a1e55b642b3e14c940aae24feaff8b

View on Chainz ↗

Height

#127,529

Difficulty

9.783817

Transactions

Size

392 B

Version

Bits

09c8a83f

Nonce

318,150

Timestamp

8/21/2013, 2:24:25 PM

Confirmations

6,688,846

Merkle Root

76e19ec7bcfe8abd86da3528b72f38f1ef8afd95e1cff27c7150b5939ebb8c1b

Transactions (2)

Coinbase43733c040a48b6…be3ccd567a4f4b

1 in → 1 out10.4400 XPM109 B

ALHant8s…3shagV1Q

02744d7fe681de…a6aa76a0837151

1 in → 2 out10.4600 XPM191 B

AYPpQbwu…KTUxctjo AGZvBxxa…shhkwtTn

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.

2.305 × 10⁹⁸(99-digit number)

23050731214410376523…50676913320063093190

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

2.305 × 10⁹⁸(99-digit number)

23050731214410376523…50676913320063093189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.305 × 10⁹⁸(99-digit number)

23050731214410376523…50676913320063093191

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

4.610 × 10⁹⁸(99-digit number)

46101462428820753047…01353826640126186379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.610 × 10⁹⁸(99-digit number)

46101462428820753047…01353826640126186381

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

9.220 × 10⁹⁸(99-digit number)

92202924857641506095…02707653280252372759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.220 × 10⁹⁸(99-digit number)

92202924857641506095…02707653280252372761

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

1.844 × 10⁹⁹(100-digit number)

18440584971528301219…05415306560504745519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.844 × 10⁹⁹(100-digit number)

18440584971528301219…05415306560504745521

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

3.688 × 10⁹⁹(100-digit number)

36881169943056602438…10830613121009491039

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 127529

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 7a6ede52ff0a8aab41384159cceedbb680a1e55b642b3e14c940aae24feaff8b

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 #127,529 on Chainz ↗

Block #127,529

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