Home/Chain Registry/Block #85,647

Block #85,647

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 2:04:05 PM · Difficulty 9.2910 · 6,703,840 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b93b874e711a551f28eec4eb370f79ac41d435408f36f8542966c96ddd2b1cfd

View on Chainz ↗

Height

#85,647

Difficulty

9.290973

Transactions

Size

1006 B

Version

Bits

094a7d3c

Nonce

35,975

Timestamp

7/27/2013, 2:04:05 PM

Confirmations

6,703,840

Merkle Root

480f2dd34bc7a9db01cfb497a4aadc0223ebed11f7dd2abc9e1d5224f121d796

Transactions (4)

Coinbasead076a1ea6a657…01f23328fb94f8

1 in → 1 out11.6000 XPM109 B

ATe7tG7X…yczDSDEp

e07cf49ea3a037…3029d7213b55bf

1 in → 2 out574.7000 XPM226 B

AYNX5Zhe…Gy4i6oz7 AJaLd4Hy…jFWGw6QR

b3303818d09c90…6b3cf42d6e06ac

2 in → 1 out23.2800 XPM271 B

AFtap2en…4d4n6Nrg

79b43db9210031…577c6a09eb712f

2 in → 1 out23.2200 XPM305 B

AYKekaiF…jZyRVoKZ

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.

5.226 × 10¹⁰⁵(106-digit number)

52265439158202644207…58712937560808399280

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

5.226 × 10¹⁰⁵(106-digit number)

52265439158202644207…58712937560808399279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.226 × 10¹⁰⁵(106-digit number)

52265439158202644207…58712937560808399281

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

1.045 × 10¹⁰⁶(107-digit number)

10453087831640528841…17425875121616798559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.045 × 10¹⁰⁶(107-digit number)

10453087831640528841…17425875121616798561

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

2.090 × 10¹⁰⁶(107-digit number)

20906175663281057682…34851750243233597119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.090 × 10¹⁰⁶(107-digit number)

20906175663281057682…34851750243233597121

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

4.181 × 10¹⁰⁶(107-digit number)

41812351326562115365…69703500486467194239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.181 × 10¹⁰⁶(107-digit number)

41812351326562115365…69703500486467194241

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

8.362 × 10¹⁰⁶(107-digit number)

83624702653124230731…39407000972934388479

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 85647

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 b93b874e711a551f28eec4eb370f79ac41d435408f36f8542966c96ddd2b1cfd

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 #85,647 on Chainz ↗