Home/Chain Registry/Block #77,498

Block #77,498

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 10:46:49 AM · Difficulty 9.1760 · 6,716,003 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d45e20c5bd5a1d1a68a3108ec9690f7c549fd3eddb65764831c853ca9bda459

View on Chainz ↗

Height

#77,498

Difficulty

9.175957

Transactions

Size

202 B

Version

Bits

092d0b7e

Nonce

514

Timestamp

7/22/2013, 10:46:49 AM

Confirmations

6,716,003

Merkle Root

dcf4c19bf06a9969f92f936d12331a3c3a1df6642d67aea7aa44dad2b598694d

Transactions (1)

Coinbasedcf4c19bf06a99…44dad2b598694d

1 in → 1 out11.8600 XPM110 B

AM1x2aFz…bDzAbbop

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.

7.897 × 10⁹⁹(100-digit number)

78973601967322309264…33599084853840103950

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

7.897 × 10⁹⁹(100-digit number)

78973601967322309264…33599084853840103949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.897 × 10⁹⁹(100-digit number)

78973601967322309264…33599084853840103951

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

1.579 × 10¹⁰⁰(101-digit number)

15794720393464461852…67198169707680207899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.579 × 10¹⁰⁰(101-digit number)

15794720393464461852…67198169707680207901

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

3.158 × 10¹⁰⁰(101-digit number)

31589440786928923705…34396339415360415799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.158 × 10¹⁰⁰(101-digit number)

31589440786928923705…34396339415360415801

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

6.317 × 10¹⁰⁰(101-digit number)

63178881573857847411…68792678830720831599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.317 × 10¹⁰⁰(101-digit number)

63178881573857847411…68792678830720831601

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

1.263 × 10¹⁰¹(102-digit number)

12635776314771569482…37585357661441663199

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 77498

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 0d45e20c5bd5a1d1a68a3108ec9690f7c549fd3eddb65764831c853ca9bda459

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 #77,498 on Chainz ↗