Home/Chain Registry/Block #162,535

Block #162,535

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/13/2013, 9:16:15 AM · Difficulty 9.8614 · 6,628,821 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de3f1a78a2566cbb29e7b6b6b515c6ada3e5a8bfdbf0ad3f2bf9e333fbe78a95

View on Chainz ↗

Height

#162,535

Difficulty

9.861428

Transactions

Size

1.27 KB

Version

Bits

09dc8684

Nonce

125,974

Timestamp

9/13/2013, 9:16:15 AM

Confirmations

6,628,821

Merkle Root

7ed07613014f5094747184362bfe1dbf21112f07d6e5ef9dde083e3168395299

Transactions (3)

Coinbasea0b4adf5778ba4…935a6776cb88be

1 in → 1 out10.2900 XPM109 B

AJHy63je…gcpU5UnY

4143d1e575c872…f06b15d5d84903

4 in → 1 out41.0700 XPM499 B

AU63Ubwp…RaoT2ZVk

bd0475f7ab96b3…ee4f2523c43821

4 in → 1 out11.0000 XPM601 B

AFz9fXym…wh4UqpkL

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.

1.003 × 10⁹⁵(96-digit number)

10033184967627878061…84771705017090041160

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

1.003 × 10⁹⁵(96-digit number)

10033184967627878061…84771705017090041159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.003 × 10⁹⁵(96-digit number)

10033184967627878061…84771705017090041161

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

2.006 × 10⁹⁵(96-digit number)

20066369935255756122…69543410034180082319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.006 × 10⁹⁵(96-digit number)

20066369935255756122…69543410034180082321

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

4.013 × 10⁹⁵(96-digit number)

40132739870511512244…39086820068360164639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.013 × 10⁹⁵(96-digit number)

40132739870511512244…39086820068360164641

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

8.026 × 10⁹⁵(96-digit number)

80265479741023024489…78173640136720329279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.026 × 10⁹⁵(96-digit number)

80265479741023024489…78173640136720329281

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

1.605 × 10⁹⁶(97-digit number)

16053095948204604897…56347280273440658559

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 162535

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 de3f1a78a2566cbb29e7b6b6b515c6ada3e5a8bfdbf0ad3f2bf9e333fbe78a95

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 #162,535 on Chainz ↗