Home/Chain Registry/Block #277,910

Block #277,910

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 6:35:23 PM · Difficulty 9.9676 · 6,516,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9b067433bcfafcfda806560728fca02710da3b2360c96b19ff00e1d488190f79

View on Chainz ↗

Height

#277,910

Difficulty

9.967559

Transactions

Size

2.08 KB

Version

Bits

09f7b1f3

Nonce

62,606

Timestamp

11/27/2013, 6:35:23 PM

Confirmations

6,516,434

Merkle Root

771da57def24172ebbc0c98033ca85c67f495921689c0f0b80dbadb623e9a195

Transactions (4)

Coinbase04ecca66efc52b…81b7583e028e90

1 in → 25 out10.0500 XPM913 B

AN8nUzff…YcDfRDQ2 AbiApRgN…g8QuFUwL ANQKf2g4…29NaVj23 AcP9aGkN…9c7TeeiQ AJHH6QuE…N3s6fxLC

342402b8863d8d…1fe45d98f8516d

3 in → 2 out9.9280 XPM521 B

AUMMT4gE…UpriaNXb AHh1gLgs…6ZzQh7Sf

89973200798b31…485fa0d6fe3549

1 in → 2 out2.5312 XPM227 B

AGTtcepQ…V6LF5d19 AKUDicKW…Jh8EkA6K

1f4b55a95b334c…73f7739eb71bf2

2 in → 2 out1.1751 XPM376 B

AGQxR1oS…2N1xAZXN AUZCkHsH…TuuCYXNe

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.

1.445 × 10⁹⁴(95-digit number)

14454421571536112997…57547811291067774080

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

1.445 × 10⁹⁴(95-digit number)

14454421571536112997…57547811291067774079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.445 × 10⁹⁴(95-digit number)

14454421571536112997…57547811291067774081

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

2.890 × 10⁹⁴(95-digit number)

28908843143072225995…15095622582135548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.890 × 10⁹⁴(95-digit number)

28908843143072225995…15095622582135548161

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

5.781 × 10⁹⁴(95-digit number)

57817686286144451991…30191245164271096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.781 × 10⁹⁴(95-digit number)

57817686286144451991…30191245164271096321

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

1.156 × 10⁹⁵(96-digit number)

11563537257228890398…60382490328542192639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.156 × 10⁹⁵(96-digit number)

11563537257228890398…60382490328542192641

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

2.312 × 10⁹⁵(96-digit number)

23127074514457780796…20764980657084385279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.312 × 10⁹⁵(96-digit number)

23127074514457780796…20764980657084385281

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 277910

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 9b067433bcfafcfda806560728fca02710da3b2360c96b19ff00e1d488190f79

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 #277,910 on Chainz ↗