Home/Chain Registry/Block #2,636,070

Block #2,636,070

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 11:05:36 AM · Difficulty 11.3593 · 4,196,140 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d177e803ca2269e4e1cdbd71e0fee9465449cf7cbaec396da21793e2a89b769f

View on Chainz ↗

Height

#2,636,070

Difficulty

11.359333

Transactions

Size

427 B

Version

Bits

0b5bfd45

Nonce

376,328,394

Timestamp

4/29/2018, 11:05:36 AM

Confirmations

4,196,140

Merkle Root

4e6ef086eabfd3eaf674f61a21ee2027e797f9002a4d9abb8abd31688e5d8488

Transactions (2)

Coinbaseefdee60ffab2d8…f7419e3f2968a1

1 in → 1 out7.7500 XPM110 B

AG1FnGiX…SutvYBVA

9013032c36d0af…06caf1436c99eb

1 in → 2 out118.7820 XPM225 B

Ad3FmMmo…Qdw3toT4 AdEHW7JP…1UVmvwuN

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.

4.904 × 10⁹⁹(100-digit number)

49046977753327718204…58953689308381839360

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

4.904 × 10⁹⁹(100-digit number)

49046977753327718204…58953689308381839359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.904 × 10⁹⁹(100-digit number)

49046977753327718204…58953689308381839361

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

9.809 × 10⁹⁹(100-digit number)

98093955506655436409…17907378616763678719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.809 × 10⁹⁹(100-digit number)

98093955506655436409…17907378616763678721

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

1.961 × 10¹⁰⁰(101-digit number)

19618791101331087281…35814757233527357439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.961 × 10¹⁰⁰(101-digit number)

19618791101331087281…35814757233527357441

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

3.923 × 10¹⁰⁰(101-digit number)

39237582202662174563…71629514467054714879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.923 × 10¹⁰⁰(101-digit number)

39237582202662174563…71629514467054714881

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

7.847 × 10¹⁰⁰(101-digit number)

78475164405324349127…43259028934109429759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.847 × 10¹⁰⁰(101-digit number)

78475164405324349127…43259028934109429761

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

1.569 × 10¹⁰¹(102-digit number)

15695032881064869825…86518057868218859519

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 2636070

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 d177e803ca2269e4e1cdbd71e0fee9465449cf7cbaec396da21793e2a89b769f

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 #2,636,070 on Chainz ↗

Block #2,636,070

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