Home/Chain Registry/Block #2,634,390

Block #2,634,390

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 9:11:38 PM · Difficulty 11.2423 · 4,196,697 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

173c496d25b6b9285e5021919f63cd8687045481cf84b6424dbc461bb8e35a40

View on Chainz ↗

Height

#2,634,390

Difficulty

11.242280

Transactions

Size

574 B

Version

Bits

0b3e0611

Nonce

1,752,753,101

Timestamp

4/28/2018, 9:11:38 PM

Confirmations

4,196,697

Merkle Root

97f3f833971edd976cf426c9db1ff611c5668e5090ad00f767ff12f40cdf1422

Transactions (2)

Coinbase0128278d5a002f…fde610e6535b1a

1 in → 1 out7.9100 XPM109 B

Adqah8zh…1WwoHJ9t

baa03d3e01e9af…a84a62143b2882

2 in → 2 out38.7851 XPM374 B

AKCSvoxS…pqXFEBhu Af4THhrU…2GZVMqJ4

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.

1.550 × 10⁹⁸(99-digit number)

15509174903980744248…46116604936306688000

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

1.550 × 10⁹⁸(99-digit number)

15509174903980744248…46116604936306687999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.550 × 10⁹⁸(99-digit number)

15509174903980744248…46116604936306688001

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

3.101 × 10⁹⁸(99-digit number)

31018349807961488496…92233209872613375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.101 × 10⁹⁸(99-digit number)

31018349807961488496…92233209872613376001

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

6.203 × 10⁹⁸(99-digit number)

62036699615922976993…84466419745226751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.203 × 10⁹⁸(99-digit number)

62036699615922976993…84466419745226752001

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

1.240 × 10⁹⁹(100-digit number)

12407339923184595398…68932839490453503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.240 × 10⁹⁹(100-digit number)

12407339923184595398…68932839490453504001

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

2.481 × 10⁹⁹(100-digit number)

24814679846369190797…37865678980907007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.481 × 10⁹⁹(100-digit number)

24814679846369190797…37865678980907008001

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

4.962 × 10⁹⁹(100-digit number)

49629359692738381594…75731357961814015999

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 2634390

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 173c496d25b6b9285e5021919f63cd8687045481cf84b6424dbc461bb8e35a40

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 #2,634,390 on Chainz ↗

Block #2,634,390

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