Home/Chain Registry/Block #160,465

Block #160,465

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 11:04:38 PM · Difficulty 9.8608 · 6,631,560 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0b5ace40dd73c807fb92e24a403d845931e104ca5f0475fc8b2c8fdda63cd498

View on Chainz ↗

Height

#160,465

Difficulty

9.860768

Transactions

Size

203 B

Version

Bits

09dc5b48

Nonce

117,441,101

Timestamp

9/11/2013, 11:04:38 PM

Confirmations

6,631,560

Merkle Root

d039c848bb8dd0e91b81ab12bb7ee4cda165a58549364fafaf5e0f802ecd1f8a

Transactions (1)

Coinbased039c848bb8dd0…5e0f802ecd1f8a

1 in → 1 out10.2700 XPM112 B

AcLBm5Z9…S683d7c3

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.

1.372 × 10⁹⁸(99-digit number)

13723740159641761393…67298916289283822240

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

1.372 × 10⁹⁸(99-digit number)

13723740159641761393…67298916289283822239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.372 × 10⁹⁸(99-digit number)

13723740159641761393…67298916289283822241

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

2.744 × 10⁹⁸(99-digit number)

27447480319283522786…34597832578567644479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.744 × 10⁹⁸(99-digit number)

27447480319283522786…34597832578567644481

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

5.489 × 10⁹⁸(99-digit number)

54894960638567045572…69195665157135288959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.489 × 10⁹⁸(99-digit number)

54894960638567045572…69195665157135288961

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

1.097 × 10⁹⁹(100-digit number)

10978992127713409114…38391330314270577919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.097 × 10⁹⁹(100-digit number)

10978992127713409114…38391330314270577921

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

2.195 × 10⁹⁹(100-digit number)

21957984255426818229…76782660628541155839

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 160465

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 0b5ace40dd73c807fb92e24a403d845931e104ca5f0475fc8b2c8fdda63cd498

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 #160,465 on Chainz ↗