Home/Chain Registry/Block #2,727,164

Block #2,727,164

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/29/2018, 8:39:06 PM · Difficulty 11.6273 · 4,114,344 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb2b8559be2753c9110967d8143df401782cba99deada9df5626ffa2b2bace82

View on Chainz ↗

Height

#2,727,164

Difficulty

11.627284

Transactions

Size

2.03 KB

Version

Bits

0ba095ad

Nonce

63,043,382

Timestamp

6/29/2018, 8:39:06 PM

Confirmations

4,114,344

Merkle Root

7a0518085b0baa34f69feaf55283ba2eec27e4333918f8b71b34cd82d2ceb0ce

Transactions (4)

Coinbase9e9c0a03fbb33d…9a6f9d6ac4b92d

1 in → 1 out7.4100 XPM110 B

AejJEfW7…XrM25VXt

9cc4031d37603c…239900579fd350

5 in → 2 out215.8683 XPM818 B

AbKFvGKV…eL3bdfEb AURG7ELZ…zjAK2j2T

a203ef0415ce1b…f91196f4bd7ada

5 in → 2 out32.9835 XPM681 B

ASqiQ4fM…ZyG2ebw1 AWp4iAg7…FUBLEm8x

6d4731f28bd155…a05df44bb942c5

2 in → 2 out5.2490 XPM375 B

Abo7hkWA…Pxgoatme AevxZoN3…fwTLU9Fn

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.

4.839 × 10⁹⁸(99-digit number)

48398306065510871797…15741001207693967360

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

4.839 × 10⁹⁸(99-digit number)

48398306065510871797…15741001207693967359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.839 × 10⁹⁸(99-digit number)

48398306065510871797…15741001207693967361

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

9.679 × 10⁹⁸(99-digit number)

96796612131021743595…31482002415387934719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.679 × 10⁹⁸(99-digit number)

96796612131021743595…31482002415387934721

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

1.935 × 10⁹⁹(100-digit number)

19359322426204348719…62964004830775869439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.935 × 10⁹⁹(100-digit number)

19359322426204348719…62964004830775869441

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

3.871 × 10⁹⁹(100-digit number)

38718644852408697438…25928009661551738879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.871 × 10⁹⁹(100-digit number)

38718644852408697438…25928009661551738881

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

7.743 × 10⁹⁹(100-digit number)

77437289704817394876…51856019323103477759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.743 × 10⁹⁹(100-digit number)

77437289704817394876…51856019323103477761

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

1.548 × 10¹⁰⁰(101-digit number)

15487457940963478975…03712038646206955519

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 2727164

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 cb2b8559be2753c9110967d8143df401782cba99deada9df5626ffa2b2bace82

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 #2,727,164 on Chainz ↗

Block #2,727,164

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