Home/Chain Registry/Block #145,354

Block #145,354

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 8:30:14 PM · Difficulty 9.8438 · 6,670,769 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

42b89340bfe5d944f4d197846742b9ef3ef82c340dfdedaa615d885fc030c5a4

View on Chainz ↗

Height

#145,354

Difficulty

9.843772

Transactions

Size

424 B

Version

Bits

09d8016a

Nonce

11,040

Timestamp

9/1/2013, 8:30:14 PM

Confirmations

6,670,769

Merkle Root

5549c0b9e39187df6bbd3021c4665f8a8fd9feb17df9ca95a7309fd811fe0acc

Transactions (2)

Coinbase758316feeeba95…94a0026b4e6437

1 in → 1 out10.3100 XPM109 B

ASki8pmA…Dwetzr7b

8d3e6857b75dc9…a72e1880ac9928

1 in → 2 out3.2604 XPM225 B

Ae4ssmDA…vZSZMfbk AKcSXGBu…WVRfPEsX

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.

9.573 × 10⁹⁴(95-digit number)

95734285784799042961…63002470323440725760

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

9.573 × 10⁹⁴(95-digit number)

95734285784799042961…63002470323440725759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.573 × 10⁹⁴(95-digit number)

95734285784799042961…63002470323440725761

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

1.914 × 10⁹⁵(96-digit number)

19146857156959808592…26004940646881451519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.914 × 10⁹⁵(96-digit number)

19146857156959808592…26004940646881451521

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

3.829 × 10⁹⁵(96-digit number)

38293714313919617184…52009881293762903039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.829 × 10⁹⁵(96-digit number)

38293714313919617184…52009881293762903041

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

7.658 × 10⁹⁵(96-digit number)

76587428627839234369…04019762587525806079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.658 × 10⁹⁵(96-digit number)

76587428627839234369…04019762587525806081

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

1.531 × 10⁹⁶(97-digit number)

15317485725567846873…08039525175051612159

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 145354

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 42b89340bfe5d944f4d197846742b9ef3ef82c340dfdedaa615d885fc030c5a4

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 #145,354 on Chainz ↗

Block #145,354

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