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Block #145,730

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 2:06:21 AM · Difficulty 9.8450 · 6,644,270 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df8a9d57beedd3a1b4639da34a49cf02b17be0290dbc0b00d79b490ba1565b27

View on Chainz ↗

Height

#145,730

Difficulty

9.845034

Transactions

Size

1.17 KB

Version

Bits

09d85427

Nonce

116,499

Timestamp

9/2/2013, 2:06:21 AM

Confirmations

6,644,270

Merkle Root

a2118a616bf1e5055ca6177bb513dca96ae802f8b2d0fe380585cfa6b38ea728

Transactions (4)

Coinbase2d71bcee0f5496…ba8bad942c5728

1 in → 1 out10.3300 XPM109 B

ATsAKghY…mNpRCdtc

6d33e83f08624b…163f35bfd6f613

4 in → 1 out44.0300 XPM502 B

AZnj4md2…F6BKcyB7

45c327200e61bb…b6d93fe2654042

2 in → 1 out22.4700 XPM272 B

AZnj4md2…F6BKcyB7

7b2a5150342338…6a7cb5d974da85

1 in → 2 out2.3230 XPM225 B

AWq6Axks…7ZKoxUPS AVtj9fEt…5iKvQNA1

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.

2.720 × 10⁹⁸(99-digit number)

27201913430542887628…83375443950232640000

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

2.720 × 10⁹⁸(99-digit number)

27201913430542887628…83375443950232639999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.720 × 10⁹⁸(99-digit number)

27201913430542887628…83375443950232640001

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

5.440 × 10⁹⁸(99-digit number)

54403826861085775256…66750887900465279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.440 × 10⁹⁸(99-digit number)

54403826861085775256…66750887900465280001

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

1.088 × 10⁹⁹(100-digit number)

10880765372217155051…33501775800930559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.088 × 10⁹⁹(100-digit number)

10880765372217155051…33501775800930560001

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

2.176 × 10⁹⁹(100-digit number)

21761530744434310102…67003551601861119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.176 × 10⁹⁹(100-digit number)

21761530744434310102…67003551601861120001

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

4.352 × 10⁹⁹(100-digit number)

43523061488868620205…34007103203722239999

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 145730

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 df8a9d57beedd3a1b4639da34a49cf02b17be0290dbc0b00d79b490ba1565b27

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 #145,730 on Chainz ↗