Home/Chain Registry/Block #86,301

Block #86,301

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 1:10:41 AM · Difficulty 9.2891 · 6,704,703 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a65aba66b4323cbb528db2e56f5de6f68c46544ffd0f3deba7157ce663c19b7

View on Chainz ↗

Height

#86,301

Difficulty

9.289120

Transactions

Size

206 B

Version

Bits

094a03c3

Nonce

128,932

Timestamp

7/28/2013, 1:10:41 AM

Confirmations

6,704,703

Merkle Root

400bd8d70e1de960aa0c61a55a17f807a661a038024ad0c2cc814cdf37690fc6

Transactions (1)

Coinbase400bd8d70e1de9…814cdf37690fc6

1 in → 1 out11.5700 XPM109 B

AcqRywNK…jBhCBFhw

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.

1.311 × 10¹¹¹(112-digit number)

13114731468477236047…87232691069603176040

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

1.311 × 10¹¹¹(112-digit number)

13114731468477236047…87232691069603176039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.311 × 10¹¹¹(112-digit number)

13114731468477236047…87232691069603176041

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

2.622 × 10¹¹¹(112-digit number)

26229462936954472094…74465382139206352079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.622 × 10¹¹¹(112-digit number)

26229462936954472094…74465382139206352081

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

5.245 × 10¹¹¹(112-digit number)

52458925873908944188…48930764278412704159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.245 × 10¹¹¹(112-digit number)

52458925873908944188…48930764278412704161

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

1.049 × 10¹¹²(113-digit number)

10491785174781788837…97861528556825408319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.049 × 10¹¹²(113-digit number)

10491785174781788837…97861528556825408321

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

2.098 × 10¹¹²(113-digit number)

20983570349563577675…95723057113650816639

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 86301

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 0a65aba66b4323cbb528db2e56f5de6f68c46544ffd0f3deba7157ce663c19b7

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 #86,301 on Chainz ↗