Home/Chain Registry/Block #2,261,398

Block #2,261,398

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/21/2017, 9:05:50 AM · Difficulty 10.9521 · 4,578,280 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e368724c12e029f08bcc9c3bfb0fdd4378f2b221ec7f346f229ddfcc933728c

View on Chainz ↗

Height

#2,261,398

Difficulty

10.952104

Transactions

Size

1.58 KB

Version

Bits

0af3bd14

Nonce

961,401,448

Timestamp

8/21/2017, 9:05:50 AM

Confirmations

4,578,280

Merkle Root

8e29eff289593c8dc6cf0045801a5223ffd077ed826ebf1e411d953df3a6343a

Transactions (4)

Coinbaseb8bfe611069743…a68e8b1fc04373

1 in → 1 out8.3500 XPM109 B

AG9e4yzZ…MjBLWWcy

3d51dd804db96d…85b68f645a143c

3 in → 2 out2967.0487 XPM525 B

AJuH7zAm…DsLPwwDn AWRDnK93…19Vviqfz

edc79c9094ea8a…ebde74262f9245

2 in → 2 out1099.9203 XPM375 B

AHXE597d…szMRJph2 AZGStUHo…ii1maJpV

4227f79e9f5130…1bef55fdfb2bbc

3 in → 2 out1484.0227 XPM521 B

AW8nLQdh…SXso8ffL AZGStUHo…ii1maJpV

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.

2.922 × 10⁹⁴(95-digit number)

29222286681881641624…15857890224613997640

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

2.922 × 10⁹⁴(95-digit number)

29222286681881641624…15857890224613997639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.922 × 10⁹⁴(95-digit number)

29222286681881641624…15857890224613997641

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

5.844 × 10⁹⁴(95-digit number)

58444573363763283248…31715780449227995279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.844 × 10⁹⁴(95-digit number)

58444573363763283248…31715780449227995281

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

1.168 × 10⁹⁵(96-digit number)

11688914672752656649…63431560898455990559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.168 × 10⁹⁵(96-digit number)

11688914672752656649…63431560898455990561

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

2.337 × 10⁹⁵(96-digit number)

23377829345505313299…26863121796911981119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.337 × 10⁹⁵(96-digit number)

23377829345505313299…26863121796911981121

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

4.675 × 10⁹⁵(96-digit number)

46755658691010626598…53726243593823962239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.675 × 10⁹⁵(96-digit number)

46755658691010626598…53726243593823962241

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 2261398

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 9e368724c12e029f08bcc9c3bfb0fdd4378f2b221ec7f346f229ddfcc933728c

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 #2,261,398 on Chainz ↗

Block #2,261,398

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