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Block #5,604,857

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2024, 2:14:04 PM · Difficulty 10.8939 · 1,237,344 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce4e4feeadb77b7741c7a4dd47455329959802c24eb519267c52a35c90078996

View on Chainz ↗

Height

#5,604,857

Difficulty

10.893901

Transactions

Size

945 B

Version

Bits

0ae4d6b9

Nonce

76,907,527

Timestamp

1/10/2024, 2:14:04 PM

Confirmations

1,237,344

Merkle Root

14323ad875f5d123d9ccbfc6e6cc2481985a52d517a6b2986f76158a02c06029

Transactions (3)

Coinbasebcf048e8ecf4c7…40990664a4ea78

1 in → 1 out8.5100 XPM109 B

AQsLiKcL…7mnzVY2H

9d103b53ce188b…d37c3f0ebc7c6f

1 in → 2 out99.9523 XPM226 B

AKhmRkX7…oYkHM1YR AdqMmmyv…WM2sjDsj

e9378160e8a317…f65af8add4b6d0

3 in → 2 out1.0214 XPM521 B

ANbunEXo…ag81unC8 AdqMmmyv…WM2sjDsj

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.

2.034 × 10⁹³(94-digit number)

20345828182994687590…91444053127788823620

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

2.034 × 10⁹³(94-digit number)

20345828182994687590…91444053127788823619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.034 × 10⁹³(94-digit number)

20345828182994687590…91444053127788823621

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

4.069 × 10⁹³(94-digit number)

40691656365989375181…82888106255577647239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.069 × 10⁹³(94-digit number)

40691656365989375181…82888106255577647241

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

8.138 × 10⁹³(94-digit number)

81383312731978750363…65776212511155294479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.138 × 10⁹³(94-digit number)

81383312731978750363…65776212511155294481

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

1.627 × 10⁹⁴(95-digit number)

16276662546395750072…31552425022310588959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.627 × 10⁹⁴(95-digit number)

16276662546395750072…31552425022310588961

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

3.255 × 10⁹⁴(95-digit number)

32553325092791500145…63104850044621177919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.255 × 10⁹⁴(95-digit number)

32553325092791500145…63104850044621177921

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 5604857

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 ce4e4feeadb77b7741c7a4dd47455329959802c24eb519267c52a35c90078996

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 #5,604,857 on Chainz ↗

Block #5,604,857

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