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Block #2,139,880

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/1/2017, 1:40:57 AM · Difficulty 10.8774 · 4,705,013 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6112bad4e29565fb29d0ad7aab81d63979e29b56f168248bc7e89c939b595538

View on Chainz ↗

Height

#2,139,880

Difficulty

10.877445

Transactions

Size

428 B

Version

Bits

0ae0a037

Nonce

241,442,815

Timestamp

6/1/2017, 1:40:57 AM

Confirmations

4,705,013

Merkle Root

3d5c9bb37839ca54a6652a9f3bf379c219f4b344e9951b333130adc4cd753e1c

Transactions (2)

Coinbasef9b00eff6b8d0c…cdaef4ccc7642f

1 in → 1 out8.4500 XPM110 B

APQztTW7…riomDwF4

d0067d87bc529b…d0fae9e0623333

1 in → 2 out5811.2900 XPM227 B

ARECL5rB…QBRZg3bH AeBMKHXa…HBDEURtz

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.

9.232 × 10⁹⁷(98-digit number)

92328492124875750269…81842633390031503360

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

9.232 × 10⁹⁷(98-digit number)

92328492124875750269…81842633390031503359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.232 × 10⁹⁷(98-digit number)

92328492124875750269…81842633390031503361

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

1.846 × 10⁹⁸(99-digit number)

18465698424975150053…63685266780063006719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.846 × 10⁹⁸(99-digit number)

18465698424975150053…63685266780063006721

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

3.693 × 10⁹⁸(99-digit number)

36931396849950300107…27370533560126013439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.693 × 10⁹⁸(99-digit number)

36931396849950300107…27370533560126013441

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

7.386 × 10⁹⁸(99-digit number)

73862793699900600215…54741067120252026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.386 × 10⁹⁸(99-digit number)

73862793699900600215…54741067120252026881

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

1.477 × 10⁹⁹(100-digit number)

14772558739980120043…09482134240504053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.477 × 10⁹⁹(100-digit number)

14772558739980120043…09482134240504053761

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 2139880

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 6112bad4e29565fb29d0ad7aab81d63979e29b56f168248bc7e89c939b595538

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 #2,139,880 on Chainz ↗

Block #2,139,880

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