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Block #858,490

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2014, 4:07:26 PM · Difficulty 10.9667 · 5,981,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6727679c266215eee2a3f2816e75bc24c2466e637bd53f184a20c50f9098e1f2

View on Chainz ↗

Height

#858,490

Difficulty

10.966664

Transactions

Size

686 B

Version

Bits

0af7774a

Nonce

349,378,924

Timestamp

12/18/2014, 4:07:26 PM

Confirmations

5,981,066

Merkle Root

0a1562f08c4b667b8b7191a628b35e0a21c6ff5ba3f71d80e32f2f6715949467

Transactions (3)

Coinbasecb92c4ab81f4e3…cde12c09d479ee

1 in → 1 out8.3300 XPM109 B

AULY2pjc…ephkB2qi

94a8ff03b9a67a…ef6a7a301c6efa

1 in → 3 out0.2478 XPM261 B

AMnDveJs…bfK7hAXn AKXsCNeg…Pj6XNy2y ARtCL1e2…JVXKNWq4

816d7df4bb8d46…7064b8c107ded8

1 in → 2 out0.0893 XPM227 B

AZaMWasW…m8ZMytV1 AJkaTmQP…9CcSbctz

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.

2.135 × 10⁹³(94-digit number)

21356060954661199084…97490482430900308490

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

2.135 × 10⁹³(94-digit number)

21356060954661199084…97490482430900308489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.135 × 10⁹³(94-digit number)

21356060954661199084…97490482430900308491

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

4.271 × 10⁹³(94-digit number)

42712121909322398168…94980964861800616979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.271 × 10⁹³(94-digit number)

42712121909322398168…94980964861800616981

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

8.542 × 10⁹³(94-digit number)

85424243818644796336…89961929723601233959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.542 × 10⁹³(94-digit number)

85424243818644796336…89961929723601233961

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

1.708 × 10⁹⁴(95-digit number)

17084848763728959267…79923859447202467919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.708 × 10⁹⁴(95-digit number)

17084848763728959267…79923859447202467921

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

3.416 × 10⁹⁴(95-digit number)

34169697527457918534…59847718894404935839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.416 × 10⁹⁴(95-digit number)

34169697527457918534…59847718894404935841

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 858490

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 6727679c266215eee2a3f2816e75bc24c2466e637bd53f184a20c50f9098e1f2

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 #858,490 on Chainz ↗

Block #858,490

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