Home/Chain Registry/Block #859,096

Block #859,096

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/19/2014, 4:16:02 AM · Difficulty 10.9659 · 5,974,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77fcc32c4381fe84be3966a3b0aa1332eac5ff8793cc7be06abe8385ae0040d2

View on Chainz ↗

Height

#859,096

Difficulty

10.965877

Transactions

Size

9.26 KB

Version

Bits

0af743bb

Nonce

756,364,811

Timestamp

12/19/2014, 4:16:02 AM

Confirmations

5,974,417

Merkle Root

bf455e4c1117eb7835a4c2be2bff7b2b484a0a3341d28dd18ab55f932511dd15

Transactions (4)

Coinbase4dd29f2bea4a80…433ae7b143dd0b

1 in → 1 out8.5800 XPM116 B

ANSXnLY2…Sd25TjkD

10fefc5a275ee9…eee930fa588f13

3 in → 2 out21.9332 XPM524 B

Ae9FMzWn…MXHdUEjJ AL5J1bvP…nMhE6L6Y

3a1fdaf4c37105…6be29aa22335f9

2 in → 2 out14.9358 XPM375 B

AHULFDoc…jFT5aLeH AeSCDTjX…MwtoboZd

ccd7dae3e978b9…b3c650f65c0cc4

56 in → 2 out21.6015 XPM8.18 KB

AQPmBqUt…fd7AM6Zd AYbQUuPy…ngBocWSr

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.

4.818 × 10⁹⁶(97-digit number)

48180617602144455528…91246252524517719040

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

4.818 × 10⁹⁶(97-digit number)

48180617602144455528…91246252524517719039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.818 × 10⁹⁶(97-digit number)

48180617602144455528…91246252524517719041

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

9.636 × 10⁹⁶(97-digit number)

96361235204288911057…82492505049035438079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.636 × 10⁹⁶(97-digit number)

96361235204288911057…82492505049035438081

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

1.927 × 10⁹⁷(98-digit number)

19272247040857782211…64985010098070876159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.927 × 10⁹⁷(98-digit number)

19272247040857782211…64985010098070876161

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

3.854 × 10⁹⁷(98-digit number)

38544494081715564423…29970020196141752319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.854 × 10⁹⁷(98-digit number)

38544494081715564423…29970020196141752321

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

7.708 × 10⁹⁷(98-digit number)

77088988163431128846…59940040392283504639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.708 × 10⁹⁷(98-digit number)

77088988163431128846…59940040392283504641

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.541 × 10⁹⁸(99-digit number)

15417797632686225769…19880080784567009279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 859096

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 77fcc32c4381fe84be3966a3b0aa1332eac5ff8793cc7be06abe8385ae0040d2

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 #859,096 on Chainz ↗

Block #859,096

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