Home/Chain Registry/Block #838,826

Block #838,826

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/3/2014, 11:00:15 PM · Difficulty 10.9749 · 5,988,441 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e47cc945ef1632a69b2d5299deddd19f258e81836e8cede7c8478791240d667

View on Chainz ↗

Height

#838,826

Difficulty

10.974851

Transactions

Size

1.30 KB

Version

Bits

0af98fd1

Nonce

43,091,290

Timestamp

12/3/2014, 11:00:15 PM

Confirmations

5,988,441

Merkle Root

f6ecc02793ef161eda2a657fc189a2cc1c89d140789352fc4a6a6e4e975e8b06

Transactions (4)

Coinbase1c2361ba512b49…e4826b3ab81749

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

25e1a4d1f4c3e3…50a0180a14fc16

2 in → 2 out16.5600 XPM374 B

ARycPRm4…pN32Ppkf ANYqNUuj…MsAaJcGp

89fdf90ce187eb…fbf1e1a1a64f93

3 in → 2 out10.3987 XPM523 B

AdarAJGy…EipY9LUa AUY54LT9…Q8pWMHVG

4dba8298b2f782…7f94c5b72c97e8

1 in → 2 out0.5983 XPM226 B

AMTvqX3a…sxpwNFyf AJcphMv5…MwAkUJhL

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.

1.753 × 10⁹⁶(97-digit number)

17533141052961174025…19031286670379811840

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

1.753 × 10⁹⁶(97-digit number)

17533141052961174025…19031286670379811839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.753 × 10⁹⁶(97-digit number)

17533141052961174025…19031286670379811841

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

3.506 × 10⁹⁶(97-digit number)

35066282105922348050…38062573340759623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.506 × 10⁹⁶(97-digit number)

35066282105922348050…38062573340759623681

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

7.013 × 10⁹⁶(97-digit number)

70132564211844696101…76125146681519247359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.013 × 10⁹⁶(97-digit number)

70132564211844696101…76125146681519247361

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

1.402 × 10⁹⁷(98-digit number)

14026512842368939220…52250293363038494719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.402 × 10⁹⁷(98-digit number)

14026512842368939220…52250293363038494721

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

2.805 × 10⁹⁷(98-digit number)

28053025684737878440…04500586726076989439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.805 × 10⁹⁷(98-digit number)

28053025684737878440…04500586726076989441

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

5.610 × 10⁹⁷(98-digit number)

56106051369475756881…09001173452153978879

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 838826

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 5e47cc945ef1632a69b2d5299deddd19f258e81836e8cede7c8478791240d667

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 #838,826 on Chainz ↗

Block #838,826

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