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Block #65,848

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 2:13:57 PM · Difficulty 8.9850 · 6,725,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74e4d054ec5a826b5587ea3c8155d4e867592920be57f0d6ad3a1aaed9efc9f3

View on Chainz ↗

Height

#65,848

Difficulty

8.985016

Transactions

Size

201 B

Version

Bits

08fc2a08

Nonce

137

Timestamp

7/19/2013, 2:13:57 PM

Confirmations

6,725,727

Merkle Root

1bde26752af353e3cc52da5a56a58b1839cf65b52daae825362d66fbd9b6780a

Transactions (1)

Coinbase1bde26752af353…2d66fbd9b6780a

1 in → 1 out12.3700 XPM110 B

ASUmFvxq…6mrDAKEZ

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.

3.393 × 10⁹⁶(97-digit number)

33932055211227814900…76005237922921667420

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

3.393 × 10⁹⁶(97-digit number)

33932055211227814900…76005237922921667419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.393 × 10⁹⁶(97-digit number)

33932055211227814900…76005237922921667421

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

6.786 × 10⁹⁶(97-digit number)

67864110422455629801…52010475845843334839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.786 × 10⁹⁶(97-digit number)

67864110422455629801…52010475845843334841

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

1.357 × 10⁹⁷(98-digit number)

13572822084491125960…04020951691686669679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.357 × 10⁹⁷(98-digit number)

13572822084491125960…04020951691686669681

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

2.714 × 10⁹⁷(98-digit number)

27145644168982251920…08041903383373339359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.714 × 10⁹⁷(98-digit number)

27145644168982251920…08041903383373339361

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

5.429 × 10⁹⁷(98-digit number)

54291288337964503841…16083806766746678719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 65848

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 74e4d054ec5a826b5587ea3c8155d4e867592920be57f0d6ad3a1aaed9efc9f3

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 #65,848 on Chainz ↗