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Block #1,212,450

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/28/2015, 11:01:14 PM · Difficulty 10.7500 · 5,629,641 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb20db216aaf280eaf14889e318e8e2e8cee2b1c4900b8dc1725b7558026b5c1

View on Chainz ↗

Height

#1,212,450

Difficulty

10.749997

Transactions

Size

574 B

Version

Bits

0abfffce

Nonce

448,203,047

Timestamp

8/28/2015, 11:01:14 PM

Confirmations

5,629,641

Merkle Root

2c5a967af38544192eac716517b1003ca85a12eab79ae74a00fd2fa5e0b102df

Transactions (2)

Coinbase272ee82878ffe3…0b92e0e433ce04

1 in → 1 out8.6500 XPM109 B

AQQE3Vji…wmFZQa2M

934ae1e8f574fc…d20bd3a923f2fd

2 in → 2 out2.2379 XPM374 B

AZKiFvCX…WLbsVDtw AcuM7XiJ…5uND8Jce

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.

5.870 × 10⁹⁷(98-digit number)

58702780791973414618…24650321676887900160

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

5.870 × 10⁹⁷(98-digit number)

58702780791973414618…24650321676887900159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.870 × 10⁹⁷(98-digit number)

58702780791973414618…24650321676887900161

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

1.174 × 10⁹⁸(99-digit number)

11740556158394682923…49300643353775800319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.174 × 10⁹⁸(99-digit number)

11740556158394682923…49300643353775800321

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

2.348 × 10⁹⁸(99-digit number)

23481112316789365847…98601286707551600639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.348 × 10⁹⁸(99-digit number)

23481112316789365847…98601286707551600641

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

4.696 × 10⁹⁸(99-digit number)

46962224633578731695…97202573415103201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.696 × 10⁹⁸(99-digit number)

46962224633578731695…97202573415103201281

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

9.392 × 10⁹⁸(99-digit number)

93924449267157463390…94405146830206402559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.392 × 10⁹⁸(99-digit number)

93924449267157463390…94405146830206402561

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 1212450

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 fb20db216aaf280eaf14889e318e8e2e8cee2b1c4900b8dc1725b7558026b5c1

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 #1,212,450 on Chainz ↗

Block #1,212,450

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