Home/Chain Registry/Block #2,631,652

Block #2,631,652

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/27/2018, 6:45:12 AM · Difficulty 11.1744 · 4,209,957 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9db4539b36332bee1e77c19d57b2df9bd43a4568cac09f8bb9e3be7ce16ef3e7

View on Chainz ↗

Height

#2,631,652

Difficulty

11.174408

Transactions

Size

1.01 KB

Version

Bits

0b2ca609

Nonce

187,112,988

Timestamp

4/27/2018, 6:45:12 AM

Confirmations

4,209,957

Merkle Root

ba3648a96f46ae18f163a7af3d37b8821859d43c09e819dbc6c35227a30bf507

Transactions (4)

Coinbase24ac7e50de2225…7c31e296be63c5

1 in → 1 out8.0300 XPM109 B

AYx3Dhs3…hKbGDKoF

5b8cd6dadee26a…b25e34b5f8bec5

3 in → 2 out23.8600 XPM421 B

AVvgHwJr…kj4Gjujc AZNx8JFm…dvnd3xXu

fcaa9b85ed35b9…6cb258766f33ca

1 in → 2 out7.9400 XPM192 B

AamnkX56…Dk9c6QCr AVpcA1Hu…nQnBqXTX

a80ef4973fee87…603acdffe6e48e

1 in → 2 out2.7740 XPM227 B

ANwtSRNc…za9KnLoD AS8fNJjU…1QViuCQV

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.

3.017 × 10⁹⁴(95-digit number)

30176327084170039196…40874649305462320160

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

3.017 × 10⁹⁴(95-digit number)

30176327084170039196…40874649305462320159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.017 × 10⁹⁴(95-digit number)

30176327084170039196…40874649305462320161

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

6.035 × 10⁹⁴(95-digit number)

60352654168340078393…81749298610924640319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.035 × 10⁹⁴(95-digit number)

60352654168340078393…81749298610924640321

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

1.207 × 10⁹⁵(96-digit number)

12070530833668015678…63498597221849280639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.207 × 10⁹⁵(96-digit number)

12070530833668015678…63498597221849280641

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

2.414 × 10⁹⁵(96-digit number)

24141061667336031357…26997194443698561279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.414 × 10⁹⁵(96-digit number)

24141061667336031357…26997194443698561281

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

4.828 × 10⁹⁵(96-digit number)

48282123334672062714…53994388887397122559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.828 × 10⁹⁵(96-digit number)

48282123334672062714…53994388887397122561

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

9.656 × 10⁹⁵(96-digit number)

96564246669344125429…07988777774794245119

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 2631652

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 9db4539b36332bee1e77c19d57b2df9bd43a4568cac09f8bb9e3be7ce16ef3e7

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 #2,631,652 on Chainz ↗

Block #2,631,652

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