Home/Chain Registry/Block #563,107

Block #563,107

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2014, 5:34:57 PM · Difficulty 10.9647 · 6,238,594 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a9ebb6ba4037a1e69ef3bbedab2b2af3299672dc04ca7da1ac163865efb6d97

View on Chainz ↗

Height

#563,107

Difficulty

10.964743

Transactions

Size

3.04 KB

Version

Bits

0af6f969

Nonce

634,252,575

Timestamp

5/26/2014, 5:34:57 PM

Confirmations

6,238,594

Merkle Root

3611aaaf13663e2cf6ec8cc9ce42d5c8f61d169c9bfd1498a55d178bc42d84e9

Transactions (4)

Coinbase6fe262a72db88e…adaad6de7e7c6d

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

787e5ff1508919…34d21685bb8bc5

16 in → 2 out160.5730 XPM2.39 KB

AKWh9vNC…zc3W9xwz AQXjpU4i…CFQ536Vz

7f2181d9a3b2d3…8d20147568d91b

1 in → 2 out3.2059 XPM226 B

AHaExXW4…YFhxHZNk ATE5Lfhw…CNL8fF6i

87b6be97b8fb34…d28465719b533f

1 in → 2 out2.0024 XPM227 B

AbYXZVvN…p4TunzW5 AS9ZCvju…bu3NEFwZ

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.

7.580 × 10⁹⁷(98-digit number)

75800692609163610827…26927744799548001640

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

7.580 × 10⁹⁷(98-digit number)

75800692609163610827…26927744799548001639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.580 × 10⁹⁷(98-digit number)

75800692609163610827…26927744799548001641

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

1.516 × 10⁹⁸(99-digit number)

15160138521832722165…53855489599096003279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.516 × 10⁹⁸(99-digit number)

15160138521832722165…53855489599096003281

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

3.032 × 10⁹⁸(99-digit number)

30320277043665444331…07710979198192006559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.032 × 10⁹⁸(99-digit number)

30320277043665444331…07710979198192006561

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

6.064 × 10⁹⁸(99-digit number)

60640554087330888662…15421958396384013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.064 × 10⁹⁸(99-digit number)

60640554087330888662…15421958396384013121

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

1.212 × 10⁹⁹(100-digit number)

12128110817466177732…30843916792768026239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.212 × 10⁹⁹(100-digit number)

12128110817466177732…30843916792768026241

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

2.425 × 10⁹⁹(100-digit number)

24256221634932355464…61687833585536052479

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 563107

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 3a9ebb6ba4037a1e69ef3bbedab2b2af3299672dc04ca7da1ac163865efb6d97

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 #563,107 on Chainz ↗