Home/Chain Registry/Block #77,952

Block #77,952

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 3:08:58 PM · Difficulty 9.2067 · 6,715,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6dae8df083406b933c4ccaf85d44380cca5c7f2b9ae82b3571dd7d676e2df141

View on Chainz ↗

Height

#77,952

Difficulty

9.206719

Transactions

Size

205 B

Version

Bits

0934eb87

Nonce

490

Timestamp

7/22/2013, 3:08:58 PM

Confirmations

6,715,074

Merkle Root

d1764a01ca9db78c7f209d4158cd6d7194173addbb257efc9d84201542443804

Transactions (1)

Coinbased1764a01ca9db7…84201542443804

1 in → 1 out11.7800 XPM110 B

Aa216dpk…Lsb77RXU

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.

2.356 × 10¹⁰⁷(108-digit number)

23561650546763449656…83193665872130087040

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

2.356 × 10¹⁰⁷(108-digit number)

23561650546763449656…83193665872130087039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.356 × 10¹⁰⁷(108-digit number)

23561650546763449656…83193665872130087041

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

4.712 × 10¹⁰⁷(108-digit number)

47123301093526899313…66387331744260174079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.712 × 10¹⁰⁷(108-digit number)

47123301093526899313…66387331744260174081

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

9.424 × 10¹⁰⁷(108-digit number)

94246602187053798627…32774663488520348159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.424 × 10¹⁰⁷(108-digit number)

94246602187053798627…32774663488520348161

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

1.884 × 10¹⁰⁸(109-digit number)

18849320437410759725…65549326977040696319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.884 × 10¹⁰⁸(109-digit number)

18849320437410759725…65549326977040696321

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

3.769 × 10¹⁰⁸(109-digit number)

37698640874821519450…31098653954081392639

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 77952

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 6dae8df083406b933c4ccaf85d44380cca5c7f2b9ae82b3571dd7d676e2df141

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 #77,952 on Chainz ↗