Home/Chain Registry/Block #494,077

Block #494,077

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 12:07:36 AM · Difficulty 10.7125 · 6,331,490 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1959ed01ff046cfbc522c71f52525dee192f8e05b67bc9404ca2d72127b5001b

View on Chainz ↗

Height

#494,077

Difficulty

10.712450

Transactions

Size

1.59 KB

Version

Bits

0ab66326

Nonce

134,725,132

Timestamp

4/16/2014, 12:07:36 AM

Confirmations

6,331,490

Merkle Root

d1ccc45dce312f6c5682773cc5b8088746621e7beeb01ca1bf3eaadc3130db00

Transactions (4)

Coinbasec556e85c6ba622…f9f020f1e3c468

1 in → 1 out8.7300 XPM116 B

AbwWkWZt…kawDhufa

9cf5423505f49a…461a552b97c3b9

6 in → 2 out25.2946 XPM967 B

AVqMgEin…3LL9aiLV APB2iJnA…LyLLLCYA

bf34ac1b2cf405…ee2252b4dd33ca

1 in → 2 out4.6320 XPM227 B

AZTWtu7f…G1KkXycn AHnQqwKD…Trir3VLk

ea0681e55d83b4…72e6bb58eecce0

1 in → 2 out1.1797 XPM226 B

AH9gAR69…avxX2yTe AVczm5aD…wBz9AzZX

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.

1.795 × 10⁹⁷(98-digit number)

17950643662676969614…27731182944670167700

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

1.795 × 10⁹⁷(98-digit number)

17950643662676969614…27731182944670167699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.795 × 10⁹⁷(98-digit number)

17950643662676969614…27731182944670167701

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

3.590 × 10⁹⁷(98-digit number)

35901287325353939228…55462365889340335399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.590 × 10⁹⁷(98-digit number)

35901287325353939228…55462365889340335401

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

7.180 × 10⁹⁷(98-digit number)

71802574650707878457…10924731778680670799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.180 × 10⁹⁷(98-digit number)

71802574650707878457…10924731778680670801

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

1.436 × 10⁹⁸(99-digit number)

14360514930141575691…21849463557361341599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.436 × 10⁹⁸(99-digit number)

14360514930141575691…21849463557361341601

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

2.872 × 10⁹⁸(99-digit number)

28721029860283151382…43698927114722683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.872 × 10⁹⁸(99-digit number)

28721029860283151382…43698927114722683201

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 494077

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 1959ed01ff046cfbc522c71f52525dee192f8e05b67bc9404ca2d72127b5001b

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 #494,077 on Chainz ↗

Block #494,077

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