Home/Chain Registry/Block #35,532

Block #35,532

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 8:12:44 AM · Difficulty 7.9945 · 6,755,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5473eb20ba0cd77c1c5447362cfc10121383851d27a677d1adf04d20bcd4c0b

View on Chainz ↗

Height

#35,532

Difficulty

7.994514

Transactions

Size

203 B

Version

Bits

07fe987c

Nonce

161

Timestamp

7/14/2013, 8:12:44 AM

Confirmations

6,755,527

Merkle Root

ad8f52f9f3d42bb937840b4c5a1b7156334a5e1b05078205c4be7b7c55c5a28d

Transactions (1)

Coinbasead8f52f9f3d42b…be7b7c55c5a28d

1 in → 1 out15.6300 XPM109 B

AQRqYBNU…SGvK648g

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.

1.619 × 10¹⁰⁵(106-digit number)

16196284865346662659…74128995501705872600

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

1.619 × 10¹⁰⁵(106-digit number)

16196284865346662659…74128995501705872599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.619 × 10¹⁰⁵(106-digit number)

16196284865346662659…74128995501705872601

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

3.239 × 10¹⁰⁵(106-digit number)

32392569730693325318…48257991003411745199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.239 × 10¹⁰⁵(106-digit number)

32392569730693325318…48257991003411745201

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

6.478 × 10¹⁰⁵(106-digit number)

64785139461386650637…96515982006823490399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.478 × 10¹⁰⁵(106-digit number)

64785139461386650637…96515982006823490401

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

1.295 × 10¹⁰⁶(107-digit number)

12957027892277330127…93031964013646980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.295 × 10¹⁰⁶(107-digit number)

12957027892277330127…93031964013646980801

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 8 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 8

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 35532

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 b5473eb20ba0cd77c1c5447362cfc10121383851d27a677d1adf04d20bcd4c0b

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 #35,532 on Chainz ↗