Home/Chain Registry/Block #359,047

Block #359,047

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 12:55:11 PM · Difficulty 10.3850 · 6,433,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f7d7a87f371ac6f9e07dfffcddacb42a9f239639ed84c0ac31348d6b506d830

View on Chainz ↗

Height

#359,047

Difficulty

10.385031

Transactions

Size

1.15 KB

Version

Bits

0a629166

Nonce

331,923

Timestamp

1/14/2014, 12:55:11 PM

Confirmations

6,433,368

Merkle Root

fc3ee27581a3a45e38fcef1ccb159863d0d7c53e914251f40930710711dea912

Transactions (4)

Coinbase4dfe9168d6348f…c5bf6dbb74e38d

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

2efe6fd6a87dac…361894cb721a24

3 in → 2 out1.0112 XPM524 B

AFzCTcJf…UgBmWipg AZhB8g4M…33t2aE4h

8a0ce01d588e12…5f418305f33c0f

1 in → 2 out8.2587 XPM227 B

AMxRBXuY…gZ9AEqR1 AJz987nj…X2bMmzq6

50183703fb6158…8a6aac7f766d7d

1 in → 2 out5.2352 XPM226 B

AaPmti7B…XVa4oSMD APM9RHdR…q27puSP8

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.

1.932 × 10⁹⁵(96-digit number)

19320789398984000528…88054441793840779520

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

1.932 × 10⁹⁵(96-digit number)

19320789398984000528…88054441793840779519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.932 × 10⁹⁵(96-digit number)

19320789398984000528…88054441793840779521

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

3.864 × 10⁹⁵(96-digit number)

38641578797968001056…76108883587681559039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.864 × 10⁹⁵(96-digit number)

38641578797968001056…76108883587681559041

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

7.728 × 10⁹⁵(96-digit number)

77283157595936002113…52217767175363118079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.728 × 10⁹⁵(96-digit number)

77283157595936002113…52217767175363118081

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

1.545 × 10⁹⁶(97-digit number)

15456631519187200422…04435534350726236159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.545 × 10⁹⁶(97-digit number)

15456631519187200422…04435534350726236161

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

3.091 × 10⁹⁶(97-digit number)

30913263038374400845…08871068701452472319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.091 × 10⁹⁶(97-digit number)

30913263038374400845…08871068701452472321

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 359047

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 4f7d7a87f371ac6f9e07dfffcddacb42a9f239639ed84c0ac31348d6b506d830

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 #359,047 on Chainz ↗