Home/Chain Registry/Block #2,786,714

Block #2,786,714

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/9/2018, 6:42:29 PM · Difficulty 11.6728 · 4,056,124 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

899ce19ec130fc04e68bcd238c42e239078ef5ff86ce226cf8dd30c39e653f60

View on Chainz ↗

Height

#2,786,714

Difficulty

11.672768

Transactions

Size

1.58 KB

Version

Bits

0bac3a7f

Nonce

731,047,498

Timestamp

8/9/2018, 6:42:29 PM

Confirmations

4,056,124

Merkle Root

ff4802bcd051c1c01bd8b2f0704ff7bb1da20e7d943973fd5172c24f8290e70d

Transactions (4)

Coinbase95336401ab1c94…3f378e86cb6a97

1 in → 1 out7.3600 XPM110 B

AGyvwJ7U…6ueao1CJ

babfa553f9efa1…3d1d57802eec2b

1 in → 2 out6.8184 XPM226 B

ARteh6zg…3FotDMtB AZu9Aj63…quRmPXQu

249ffbb458deac…cb78d6c3a7a74b

1 in → 2 out6.3155 XPM225 B

ALg819eB…kvTf2Fuz AL79vRke…R2RSG9Vz

e7d26c2371e3f3…ace5e97d7b41e9

6 in → 2 out4.1457 XPM966 B

AQiXCaZE…Q1xa653V AdGFnV3a…o6n2zX3x

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.

5.488 × 10⁹⁷(98-digit number)

54880383780323566402…51613804238227374080

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

5.488 × 10⁹⁷(98-digit number)

54880383780323566402…51613804238227374079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.488 × 10⁹⁷(98-digit number)

54880383780323566402…51613804238227374081

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

1.097 × 10⁹⁸(99-digit number)

10976076756064713280…03227608476454748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.097 × 10⁹⁸(99-digit number)

10976076756064713280…03227608476454748161

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

2.195 × 10⁹⁸(99-digit number)

21952153512129426561…06455216952909496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.195 × 10⁹⁸(99-digit number)

21952153512129426561…06455216952909496321

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

4.390 × 10⁹⁸(99-digit number)

43904307024258853122…12910433905818992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.390 × 10⁹⁸(99-digit number)

43904307024258853122…12910433905818992641

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

8.780 × 10⁹⁸(99-digit number)

87808614048517706244…25820867811637985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.780 × 10⁹⁸(99-digit number)

87808614048517706244…25820867811637985281

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

1.756 × 10⁹⁹(100-digit number)

17561722809703541248…51641735623275970559

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 2786714

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 899ce19ec130fc04e68bcd238c42e239078ef5ff86ce226cf8dd30c39e653f60

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 #2,786,714 on Chainz ↗

Block #2,786,714

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