Home/Chain Registry/Block #1,188,236

Block #1,188,236

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/9/2015, 5:09:07 PM · Difficulty 10.8746 · 5,656,854 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c840885bb17044826985f4dcedd851aa8aa200fed77cff43c89df64abe981f0

View on Chainz ↗

Height

#1,188,236

Difficulty

10.874573

Transactions

Size

2.87 KB

Version

Bits

0adfe408

Nonce

1,313,096,796

Timestamp

8/9/2015, 5:09:07 PM

Confirmations

5,656,854

Merkle Root

53deef34a9aad076197291dbf0a856141833a0fa30776e5cefe114a8fc07ecb6

Transactions (4)

Coinbase7a99817084963f…8bfae8842309e7

1 in → 1 out8.4800 XPM109 B

AJb8WRKP…Siqvd29d

e209106ebb57ca…ae3156a725e2fc

12 in → 2 out100.8400 XPM1.81 KB

AL3sue1c…JJWisfPB AXhsX5xX…q2ccbLP5

98808b11863c67…b913df30b91a5d

1 in → 2 out4.1580 XPM226 B

ANqoHvj4…B1EdKkpd AcuM7XiJ…5uND8Jce

cdad91e15f35c7…1e36130b964ee5

4 in → 2 out1.0520 XPM668 B

ALSdJSqW…iuEEePYS AXrTw46X…e1dGvSFf

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.

8.693 × 10⁹³(94-digit number)

86938971688399425283…90056725828638150040

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

8.693 × 10⁹³(94-digit number)

86938971688399425283…90056725828638150039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.693 × 10⁹³(94-digit number)

86938971688399425283…90056725828638150041

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

1.738 × 10⁹⁴(95-digit number)

17387794337679885056…80113451657276300079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.738 × 10⁹⁴(95-digit number)

17387794337679885056…80113451657276300081

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

3.477 × 10⁹⁴(95-digit number)

34775588675359770113…60226903314552600159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.477 × 10⁹⁴(95-digit number)

34775588675359770113…60226903314552600161

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

6.955 × 10⁹⁴(95-digit number)

69551177350719540227…20453806629105200319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.955 × 10⁹⁴(95-digit number)

69551177350719540227…20453806629105200321

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

1.391 × 10⁹⁵(96-digit number)

13910235470143908045…40907613258210400639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.391 × 10⁹⁵(96-digit number)

13910235470143908045…40907613258210400641

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 1188236

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 2c840885bb17044826985f4dcedd851aa8aa200fed77cff43c89df64abe981f0

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 #1,188,236 on Chainz ↗

Block #1,188,236

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