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Block #959,569

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2015, 7:30:17 AM · Difficulty 10.8880 · 5,834,803 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc94a4d3505e84ccff2ea844fb95667fbf3c11d7a7fb45728c5e02b96089f6c2

View on Chainz ↗

Height

#959,569

Difficulty

10.887956

Transactions

Size

658 B

Version

Bits

0ae3511d

Nonce

400,856,861

Timestamp

3/3/2015, 7:30:17 AM

Confirmations

5,834,803

Merkle Root

25542bc17adaf90ce9513f3377db75837f1b1547c5f2119c0d62274bd0a98376

Transactions (3)

Coinbasec334e9bbd2c18f…b5cbfd5678945b

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

628161cdb856a2…dbdc4ba7c8853a

1 in → 2 out8.3900 XPM225 B

ANfmUrFA…kVSzdPqM AbMewdtq…HcWEiEbe

a0c416dd68defc…bb7739de684597

1 in → 2 out8.3900 XPM226 B

AZwv5fv2…wcxptueF AKKnFqop…xxu5XWDy

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.

3.946 × 10⁹⁶(97-digit number)

39465927906720937634…29844900541838070400

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

3.946 × 10⁹⁶(97-digit number)

39465927906720937634…29844900541838070399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.946 × 10⁹⁶(97-digit number)

39465927906720937634…29844900541838070401

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

7.893 × 10⁹⁶(97-digit number)

78931855813441875268…59689801083676140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.893 × 10⁹⁶(97-digit number)

78931855813441875268…59689801083676140801

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

1.578 × 10⁹⁷(98-digit number)

15786371162688375053…19379602167352281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.578 × 10⁹⁷(98-digit number)

15786371162688375053…19379602167352281601

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

3.157 × 10⁹⁷(98-digit number)

31572742325376750107…38759204334704563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.157 × 10⁹⁷(98-digit number)

31572742325376750107…38759204334704563201

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

6.314 × 10⁹⁷(98-digit number)

63145484650753500214…77518408669409126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.314 × 10⁹⁷(98-digit number)

63145484650753500214…77518408669409126401

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 959569

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 fc94a4d3505e84ccff2ea844fb95667fbf3c11d7a7fb45728c5e02b96089f6c2

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 #959,569 on Chainz ↗