Home/Chain Registry/Block #58,778

Block #58,778

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 10:35:22 PM · Difficulty 8.9617 · 6,758,549 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f826a0eb657aea6b1bf30e543ef27591467042e6076e3a5d285ea46cc04549d4

View on Chainz ↗

Height

#58,778

Difficulty

8.961676

Transactions

Size

1.96 KB

Version

Bits

08f6306d

Nonce

787

Timestamp

7/17/2013, 10:35:22 PM

Confirmations

6,758,549

Merkle Root

496f0340eee60d2df52e7ef7cb1d5c8e6ad0a0d7ec161c684eaefff7a9d986f9

Transactions (3)

Coinbase4cd463ef9e8b1a…b7db6f7c748bc5

1 in → 1 out12.4600 XPM110 B

AcuRhoVu…6Pu86km9

213a5685524c8f…23abf3d759064b

8 in → 2 out71.8600 XPM1.16 KB

AGcbUTFe…Nwe6EFm6 AHkR8E3X…oT5C8e2V

30e0083972fc1a…14c9628a26a4d0

4 in → 1 out13.0000 XPM603 B

AJEaFcP5…1qv2MjaG

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.

8.046 × 10¹¹⁰(111-digit number)

80469337171934797248…41994203364815679760

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

8.046 × 10¹¹⁰(111-digit number)

80469337171934797248…41994203364815679759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.046 × 10¹¹⁰(111-digit number)

80469337171934797248…41994203364815679761

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

1.609 × 10¹¹¹(112-digit number)

16093867434386959449…83988406729631359519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.609 × 10¹¹¹(112-digit number)

16093867434386959449…83988406729631359521

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

3.218 × 10¹¹¹(112-digit number)

32187734868773918899…67976813459262719039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.218 × 10¹¹¹(112-digit number)

32187734868773918899…67976813459262719041

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

6.437 × 10¹¹¹(112-digit number)

64375469737547837798…35953626918525438079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.437 × 10¹¹¹(112-digit number)

64375469737547837798…35953626918525438081

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

1.287 × 10¹¹²(113-digit number)

12875093947509567559…71907253837050876159

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 58778

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 f826a0eb657aea6b1bf30e543ef27591467042e6076e3a5d285ea46cc04549d4

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 #58,778 on Chainz ↗

Block #58,778

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