Home/Chain Registry/Block #87,430

Block #87,430

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 9:33:08 PM · Difficulty 9.2757 · 6,703,877 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd77e196f1ec884775a85a860f7260bc9d44ce01c0cf1f4390a3c1d9732b77c8

View on Chainz ↗

Height

#87,430

Difficulty

9.275746

Transactions

Size

205 B

Version

Bits

0946974a

Nonce

117,860

Timestamp

7/28/2013, 9:33:08 PM

Confirmations

6,703,877

Merkle Root

6c05ec4eeb0a49a551eabe6d7896588404164ad545975c5a501ac29adfec6176

Transactions (1)

Coinbase6c05ec4eeb0a49…1ac29adfec6176

1 in → 1 out11.6100 XPM109 B

APF1sEZg…dnYfVHQZ

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.

1.858 × 10¹⁰⁹(110-digit number)

18589512977103979119…78209137638339447070

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

1.858 × 10¹⁰⁹(110-digit number)

18589512977103979119…78209137638339447069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.858 × 10¹⁰⁹(110-digit number)

18589512977103979119…78209137638339447071

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

3.717 × 10¹⁰⁹(110-digit number)

37179025954207958238…56418275276678894139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.717 × 10¹⁰⁹(110-digit number)

37179025954207958238…56418275276678894141

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

7.435 × 10¹⁰⁹(110-digit number)

74358051908415916476…12836550553357788279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.435 × 10¹⁰⁹(110-digit number)

74358051908415916476…12836550553357788281

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

1.487 × 10¹¹⁰(111-digit number)

14871610381683183295…25673101106715576559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.487 × 10¹¹⁰(111-digit number)

14871610381683183295…25673101106715576561

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

2.974 × 10¹¹⁰(111-digit number)

29743220763366366590…51346202213431153119

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 87430

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 cd77e196f1ec884775a85a860f7260bc9d44ce01c0cf1f4390a3c1d9732b77c8

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 #87,430 on Chainz ↗