Home/Chain Registry/Block #526,869

Block #526,869

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/5/2014, 4:04:22 PM · Difficulty 10.8835 · 6,287,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86e41224f2fa1fbe18319328f1feda26e2cbb35084d8fc4b7c3a39dd305c47ee

View on Chainz ↗

Height

#526,869

Difficulty

10.883506

Transactions

Size

880 B

Version

Bits

0ae22d70

Nonce

229,421

Timestamp

5/5/2014, 4:04:22 PM

Confirmations

6,287,262

Merkle Root

04ea86e62e0cc3acc1bc85b222992f441fc2953323ef87fd33cd41493845d511

Transactions (4)

Coinbaseff73b53bcb7ecb…c800f6a10f74ed

1 in → 1 out8.4600 XPM110 B

AeKNrjNj…1NEq95Ta

4e196464f398b4…46367ffa6f6ef0

1 in → 2 out6.0835 XPM225 B

AXkMWrT9…KvSPKK7L AZHR15HX…P2fH5VcH

c906bc3e93ada3…08a5c716793632

1 in → 2 out2.8242 XPM226 B

AM8GuxnN…AfjbhWoV AREYKoNR…GGH3uG1E

122f8aa2b1ae36…e2e09fbd54e396

1 in → 2 out2.1676 XPM226 B

AduX2gMy…KRHmdwQB Aa5KSvSy…DCwz8TMP

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.

1.783 × 10¹⁰²(103-digit number)

17831479399421302709…90422002017426786560

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

1.783 × 10¹⁰²(103-digit number)

17831479399421302709…90422002017426786559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.783 × 10¹⁰²(103-digit number)

17831479399421302709…90422002017426786561

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

3.566 × 10¹⁰²(103-digit number)

35662958798842605419…80844004034853573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.566 × 10¹⁰²(103-digit number)

35662958798842605419…80844004034853573121

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

7.132 × 10¹⁰²(103-digit number)

71325917597685210839…61688008069707146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.132 × 10¹⁰²(103-digit number)

71325917597685210839…61688008069707146241

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

1.426 × 10¹⁰³(104-digit number)

14265183519537042167…23376016139414292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.426 × 10¹⁰³(104-digit number)

14265183519537042167…23376016139414292481

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

2.853 × 10¹⁰³(104-digit number)

28530367039074084335…46752032278828584959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.853 × 10¹⁰³(104-digit number)

28530367039074084335…46752032278828584961

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 526869

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 86e41224f2fa1fbe18319328f1feda26e2cbb35084d8fc4b7c3a39dd305c47ee

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 #526,869 on Chainz ↗

Block #526,869

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