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Block #1,605,220

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2016, 2:03:08 PM · Difficulty 10.6002 · 5,240,007 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa7a7420a200c9004673c0cbfbe1f14a1a600f56b546fe9061b61efd95027b63

View on Chainz ↗

Height

#1,605,220

Difficulty

10.600243

Transactions

Size

1.25 KB

Version

Bits

0a99a98c

Nonce

507,375,485

Timestamp

5/29/2016, 2:03:08 PM

Confirmations

5,240,007

Merkle Root

4eed39a92edfd2639afc388dd6f6e05d416935ed0adeaabda3da6b44fb9056d3

Transactions (2)

Coinbase0e9a56163cf366…4e8dfecb4868a0

1 in → 1 out8.9100 XPM110 B

AXdgjit2…yNatA3JU

512d65360e959a…8982c323e84404

1 in → 27 out225.8730 XPM1.05 KB

AeZ2Armp…M5R78S3T ANT6FYei…mwuM7Nif AQ3uAoVE…gkgEyiPv AKtN3iq8…WCtmzLvh AeXndF8L…VYjXuwhk

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.

6.815 × 10⁹³(94-digit number)

68150477703204062030…57364662420151397120

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

6.815 × 10⁹³(94-digit number)

68150477703204062030…57364662420151397119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.815 × 10⁹³(94-digit number)

68150477703204062030…57364662420151397121

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

1.363 × 10⁹⁴(95-digit number)

13630095540640812406…14729324840302794239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.363 × 10⁹⁴(95-digit number)

13630095540640812406…14729324840302794241

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

2.726 × 10⁹⁴(95-digit number)

27260191081281624812…29458649680605588479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.726 × 10⁹⁴(95-digit number)

27260191081281624812…29458649680605588481

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

5.452 × 10⁹⁴(95-digit number)

54520382162563249624…58917299361211176959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.452 × 10⁹⁴(95-digit number)

54520382162563249624…58917299361211176961

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

1.090 × 10⁹⁵(96-digit number)

10904076432512649924…17834598722422353919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.090 × 10⁹⁵(96-digit number)

10904076432512649924…17834598722422353921

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 1605220

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 fa7a7420a200c9004673c0cbfbe1f14a1a600f56b546fe9061b61efd95027b63

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 #1,605,220 on Chainz ↗

Block #1,605,220

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