Home/Chain Registry/Block #77,376

Block #77,376

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 9:43:31 AM · Difficulty 9.1663 · 6,714,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6aa58cdd8f2765b8fc6986c0346efe566583839cb173f38bd75b2df55e5ac304

View on Chainz ↗

Height

#77,376

Difficulty

9.166328

Transactions

Size

427 B

Version

Bits

092a947a

Nonce

Timestamp

7/22/2013, 9:43:31 AM

Confirmations

6,714,550

Merkle Root

003aa60397d7e8977df999f5c5e288dcd8af870f463019b9beeea58f839f397d

Transactions (2)

Coinbase04e024372cce4e…152377922cdd7e

1 in → 1 out11.8900 XPM110 B

AZ27p3Cq…kmUCt4Mk

2301886bf73df6…21483a7696b0d3

1 in → 2 out99.9800 XPM225 B

ALYeDnrW…Ktfp5ahN AYfyfvKa…4LYMkVa5

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.

1.551 × 10¹⁰⁰(101-digit number)

15518395953747114385…89429844323833491550

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

1.551 × 10¹⁰⁰(101-digit number)

15518395953747114385…89429844323833491549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.551 × 10¹⁰⁰(101-digit number)

15518395953747114385…89429844323833491551

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

3.103 × 10¹⁰⁰(101-digit number)

31036791907494228770…78859688647666983099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.103 × 10¹⁰⁰(101-digit number)

31036791907494228770…78859688647666983101

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

6.207 × 10¹⁰⁰(101-digit number)

62073583814988457541…57719377295333966199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.207 × 10¹⁰⁰(101-digit number)

62073583814988457541…57719377295333966201

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

1.241 × 10¹⁰¹(102-digit number)

12414716762997691508…15438754590667932399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.241 × 10¹⁰¹(102-digit number)

12414716762997691508…15438754590667932401

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

2.482 × 10¹⁰¹(102-digit number)

24829433525995383016…30877509181335864799

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 77376

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 6aa58cdd8f2765b8fc6986c0346efe566583839cb173f38bd75b2df55e5ac304

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 #77,376 on Chainz ↗