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Block #1,534,820

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 12:02:29 PM · Difficulty 10.6187 · 5,292,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0f47d85f73b4feb98e5c12d8778a7de0ed7d67b0a70ede95e88e4d2ad70edf1

View on Chainz ↗

Height

#1,534,820

Difficulty

10.618740

Transactions

Size

22.44 KB

Version

Bits

0a9e65bb

Nonce

1,077,719,581

Timestamp

4/10/2016, 12:02:29 PM

Confirmations

5,292,272

Merkle Root

5963be5e49e68f9e53734b5e5ae5d8912113ce9d7139ef72f795adc487eb758d

Transactions (4)

Coinbase64b909b4d73ecd…e74b3f4dba4446

1 in → 1 out9.0900 XPM109 B

AGCub8M5…xUQQCPkF

f9bb6baf22b594…9933dac6a131f1

51 in → 1 out267.1057 XPM7.42 KB

AbwTKMmC…Y5wUc72G

fa64c55fffc76a…1bd20f059b1a9b

51 in → 1 out150.6384 XPM7.41 KB

AWj2mt3J…MDNjcMhA

b461790a6c596f…35eba15b5e4c59

51 in → 1 out3223.0542 XPM7.42 KB

AHkaK4PA…uzb9WTgR

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.

4.931 × 10⁹³(94-digit number)

49314562534360094415…51281346439439763200

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

4.931 × 10⁹³(94-digit number)

49314562534360094415…51281346439439763199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.931 × 10⁹³(94-digit number)

49314562534360094415…51281346439439763201

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

9.862 × 10⁹³(94-digit number)

98629125068720188830…02562692878879526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.862 × 10⁹³(94-digit number)

98629125068720188830…02562692878879526401

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

1.972 × 10⁹⁴(95-digit number)

19725825013744037766…05125385757759052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.972 × 10⁹⁴(95-digit number)

19725825013744037766…05125385757759052801

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

3.945 × 10⁹⁴(95-digit number)

39451650027488075532…10250771515518105599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.945 × 10⁹⁴(95-digit number)

39451650027488075532…10250771515518105601

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

7.890 × 10⁹⁴(95-digit number)

78903300054976151064…20501543031036211199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.890 × 10⁹⁴(95-digit number)

78903300054976151064…20501543031036211201

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 1534820

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 c0f47d85f73b4feb98e5c12d8778a7de0ed7d67b0a70ede95e88e4d2ad70edf1

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 #1,534,820 on Chainz ↗

Block #1,534,820

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