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Block #59,431

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 2:06:45 AM · Difficulty 8.9649 · 6,766,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a568b4c1b4d5370df8fc82f9c6da51fc2dc8f4f945559d908d972871bd5f52bd

View on Chainz ↗

Height

#59,431

Difficulty

8.964902

Transactions

Size

209 B

Version

Bits

08f703d5

Nonce

865

Timestamp

7/18/2013, 2:06:45 AM

Confirmations

6,766,262

Merkle Root

2d1af8039b62c8eaecede9a9b903df669467da0f3be12734673407689659b4e6

Transactions (1)

Coinbase2d1af8039b62c8…3407689659b4e6

1 in → 1 out12.4300 XPM110 B

ALXjrugC…hByoynjy

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.

1.027 × 10¹¹⁶(117-digit number)

10278488815907652887…90994027799143115500

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

1.027 × 10¹¹⁶(117-digit number)

10278488815907652887…90994027799143115499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.027 × 10¹¹⁶(117-digit number)

10278488815907652887…90994027799143115501

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

2.055 × 10¹¹⁶(117-digit number)

20556977631815305774…81988055598286230999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.055 × 10¹¹⁶(117-digit number)

20556977631815305774…81988055598286231001

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

4.111 × 10¹¹⁶(117-digit number)

41113955263630611549…63976111196572461999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.111 × 10¹¹⁶(117-digit number)

41113955263630611549…63976111196572462001

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

8.222 × 10¹¹⁶(117-digit number)

82227910527261223099…27952222393144923999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.222 × 10¹¹⁶(117-digit number)

82227910527261223099…27952222393144924001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

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 59431

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 a568b4c1b4d5370df8fc82f9c6da51fc2dc8f4f945559d908d972871bd5f52bd

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 #59,431 on Chainz ↗

Block #59,431

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