Home/Chain Registry/Block #83,667

Block #83,667

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 7:40:55 AM · Difficulty 9.2682 · 6,709,579 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c71241ec0947c23df709e5a4b1cee559be815cbc1a951bc525f2b022614ac49e

View on Chainz ↗

Height

#83,667

Difficulty

9.268235

Transactions

Size

356 B

Version

Bits

0944ab0c

Nonce

22,970

Timestamp

7/26/2013, 7:40:55 AM

Confirmations

6,709,579

Merkle Root

36736eacea91cd12b7704db07a878fbe976316a7ec3b22790aa8c6b877deb477

Transactions (2)

Coinbasec92b07c07174c8…afd9a82942b680

1 in → 1 out11.6300 XPM109 B

ATe7tG7X…yczDSDEp

2db38e7e31ac5a…8b5b7f33ab0000

1 in → 1 out11.6700 XPM159 B

AbhWjNtr…ZGT63E3Y

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.

2.095 × 10⁹⁰(91-digit number)

20957539395338453585…83981492784444157040

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

2.095 × 10⁹⁰(91-digit number)

20957539395338453585…83981492784444157039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.095 × 10⁹⁰(91-digit number)

20957539395338453585…83981492784444157041

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

4.191 × 10⁹⁰(91-digit number)

41915078790676907171…67962985568888314079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.191 × 10⁹⁰(91-digit number)

41915078790676907171…67962985568888314081

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

8.383 × 10⁹⁰(91-digit number)

83830157581353814342…35925971137776628159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.383 × 10⁹⁰(91-digit number)

83830157581353814342…35925971137776628161

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

1.676 × 10⁹¹(92-digit number)

16766031516270762868…71851942275553256319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.676 × 10⁹¹(92-digit number)

16766031516270762868…71851942275553256321

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

3.353 × 10⁹¹(92-digit number)

33532063032541525737…43703884551106512639

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 83667

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 c71241ec0947c23df709e5a4b1cee559be815cbc1a951bc525f2b022614ac49e

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 #83,667 on Chainz ↗