Home/Chain Registry/Block #562,662

Block #562,662

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2014, 6:59:36 AM · Difficulty 10.9660 · 6,232,850 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcc67a722fe8bc92247a2635fa4181d2e39f7a2c20700e1d19bea7f79846a321

View on Chainz ↗

Height

#562,662

Difficulty

10.966030

Transactions

Size

244 B

Version

Bits

0af74dc2

Nonce

640,059,216

Timestamp

5/26/2014, 6:59:36 AM

Confirmations

6,232,850

Merkle Root

a3876fcce5c1caaae8ad5f834d18eb106bcbe80df42fd9dba47d35f6af7de4a4

Transactions (1)

Coinbasea3876fcce5c1ca…7d35f6af7de4a4

1 in → 2 out8.3000 XPM152 B

AWTXTqyv…wU6unC9A ALPu3s2c…EJXLjVFh

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.

3.158 × 10¹⁰⁰(101-digit number)

31588619260215480264…78274139002883932160

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

3.158 × 10¹⁰⁰(101-digit number)

31588619260215480264…78274139002883932159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.158 × 10¹⁰⁰(101-digit number)

31588619260215480264…78274139002883932161

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

6.317 × 10¹⁰⁰(101-digit number)

63177238520430960528…56548278005767864319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.317 × 10¹⁰⁰(101-digit number)

63177238520430960528…56548278005767864321

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

1.263 × 10¹⁰¹(102-digit number)

12635447704086192105…13096556011535728639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.263 × 10¹⁰¹(102-digit number)

12635447704086192105…13096556011535728641

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

2.527 × 10¹⁰¹(102-digit number)

25270895408172384211…26193112023071457279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.527 × 10¹⁰¹(102-digit number)

25270895408172384211…26193112023071457281

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

5.054 × 10¹⁰¹(102-digit number)

50541790816344768422…52386224046142914559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.054 × 10¹⁰¹(102-digit number)

50541790816344768422…52386224046142914561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.010 × 10¹⁰²(103-digit number)

10108358163268953684…04772448092285829119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 562662

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 fcc67a722fe8bc92247a2635fa4181d2e39f7a2c20700e1d19bea7f79846a321

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 #562,662 on Chainz ↗