Home/Chain Registry/Block #106,854

Block #106,854

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/9/2013, 5:26:43 AM · Difficulty 9.6173 · 6,685,443 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65e12be71c923df97d9db694d6f1e27d2f558126aa2317ba573a7b8f451b896c

View on Chainz ↗

Height

#106,854

Difficulty

9.617334

Transactions

Size

876 B

Version

Bits

099e0993

Nonce

15,282

Timestamp

8/9/2013, 5:26:43 AM

Confirmations

6,685,443

Merkle Root

6f9d5eee2fe065d59fddce02cfb050acdeaf42c8c37b75239d15bf54cce780cf

Transactions (2)

Coinbasef89ba082bda992…2f1383417668a6

1 in → 1 out10.8100 XPM109 B

AZLchzyL…3hqTF23A

427eb44d49b13e…e6fcf4af6ae30a

4 in → 2 out120.0109 XPM669 B

AcWxiJYv…LPH1Kib5 ALYD4CvG…f8BVP7NJ

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.

9.256 × 10¹¹⁴(115-digit number)

92564534780745706916…18008084111841301790

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

9.256 × 10¹¹⁴(115-digit number)

92564534780745706916…18008084111841301789

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.256 × 10¹¹⁴(115-digit number)

92564534780745706916…18008084111841301791

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

1.851 × 10¹¹⁵(116-digit number)

18512906956149141383…36016168223682603579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.851 × 10¹¹⁵(116-digit number)

18512906956149141383…36016168223682603581

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

3.702 × 10¹¹⁵(116-digit number)

37025813912298282766…72032336447365207159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.702 × 10¹¹⁵(116-digit number)

37025813912298282766…72032336447365207161

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

7.405 × 10¹¹⁵(116-digit number)

74051627824596565533…44064672894730414319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.405 × 10¹¹⁵(116-digit number)

74051627824596565533…44064672894730414321

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

1.481 × 10¹¹⁶(117-digit number)

14810325564919313106…88129345789460828639

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 106854

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 65e12be71c923df97d9db694d6f1e27d2f558126aa2317ba573a7b8f451b896c

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 #106,854 on Chainz ↗