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Block #278,274

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 10:14:34 PM · Difficulty 9.9685 · 6,514,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a57cdc8d8650a60c3af7541db64714310f85982dd819b6bbccf82eb7532f02f0

View on Chainz ↗

Height

#278,274

Difficulty

9.968488

Transactions

Size

1.05 KB

Version

Bits

09f7eed4

Nonce

16,500

Timestamp

11/27/2013, 10:14:34 PM

Confirmations

6,514,394

Merkle Root

159e20544e7d1961b26be791a4695336995e9e138af8a5c0a867c00d7e7b5e27

Transactions (1)

Coinbase159e20544e7d19…67c00d7e7b5e27

1 in → 27 out10.0500 XPM981 B

AY9F7Byy…EfAVw9Yf ANKe4gqX…i5S2smrX AN8nUzff…YcDfRDQ2 ANoKyXcK…jYj9bWBE ALFWpHxd…zhX7LjhL

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.

9.705 × 10⁹⁴(95-digit number)

97051891546408111697…04195201412680196480

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

9.705 × 10⁹⁴(95-digit number)

97051891546408111697…04195201412680196479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.705 × 10⁹⁴(95-digit number)

97051891546408111697…04195201412680196481

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

1.941 × 10⁹⁵(96-digit number)

19410378309281622339…08390402825360392959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.941 × 10⁹⁵(96-digit number)

19410378309281622339…08390402825360392961

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

3.882 × 10⁹⁵(96-digit number)

38820756618563244678…16780805650720785919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.882 × 10⁹⁵(96-digit number)

38820756618563244678…16780805650720785921

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

7.764 × 10⁹⁵(96-digit number)

77641513237126489357…33561611301441571839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.764 × 10⁹⁵(96-digit number)

77641513237126489357…33561611301441571841

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

1.552 × 10⁹⁶(97-digit number)

15528302647425297871…67123222602883143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.552 × 10⁹⁶(97-digit number)

15528302647425297871…67123222602883143681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 278274

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 a57cdc8d8650a60c3af7541db64714310f85982dd819b6bbccf82eb7532f02f0

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 #278,274 on Chainz ↗