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Block #141,476

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 8:27:12 AM · Difficulty 9.8348 · 6,648,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09ccdc0999e21d094d8de6384f071c73332ce3dcd346854928d4026c2e7071a4

View on Chainz ↗

Height

#141,476

Difficulty

9.834847

Transactions

Size

198 B

Version

Bits

09d5b890

Nonce

130,262

Timestamp

8/30/2013, 8:27:12 AM

Confirmations

6,648,351

Merkle Root

83afd413a51fc70dad7e234f071b10a81c02fae07c6e9a7189b8c65241f54451

Transactions (1)

Coinbase83afd413a51fc7…b8c65241f54451

1 in → 1 out10.3200 XPM109 B

AeLjYwoN…qGBxBQFd

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.

8.139 × 10⁹²(93-digit number)

81393138145191662288…11379332325886090550

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

8.139 × 10⁹²(93-digit number)

81393138145191662288…11379332325886090549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.139 × 10⁹²(93-digit number)

81393138145191662288…11379332325886090551

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

1.627 × 10⁹³(94-digit number)

16278627629038332457…22758664651772181099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.627 × 10⁹³(94-digit number)

16278627629038332457…22758664651772181101

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

3.255 × 10⁹³(94-digit number)

32557255258076664915…45517329303544362199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.255 × 10⁹³(94-digit number)

32557255258076664915…45517329303544362201

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

6.511 × 10⁹³(94-digit number)

65114510516153329830…91034658607088724399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.511 × 10⁹³(94-digit number)

65114510516153329830…91034658607088724401

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

1.302 × 10⁹⁴(95-digit number)

13022902103230665966…82069317214177448799

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 141476

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 09ccdc0999e21d094d8de6384f071c73332ce3dcd346854928d4026c2e7071a4

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 #141,476 on Chainz ↗