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Block #1,535,785

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/11/2016, 3:05:37 AM · Difficulty 10.6233 · 5,307,817 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c20c79a893bbb21c339e46bd3e7a9a3f3a9757ae8eecf66e1b871bc5c2635142

View on Chainz ↗

Height

#1,535,785

Difficulty

10.623330

Transactions

Size

970 B

Version

Bits

0a9f9296

Nonce

544,798,996

Timestamp

4/11/2016, 3:05:37 AM

Confirmations

5,307,817

Merkle Root

cea860905cf4b09dd6205a3635c32fd233af0617e2018d5aa0398d1c8fbda01d

Transactions (2)

Coinbasecc61562e2a046a…b8300a73cfc115

1 in → 1 out8.8600 XPM110 B

ALXpZ5Fs…5TmpVDgJ

b790c55c2e48f6…3507a0ae423c0e

1 in → 18 out95.8429 XPM769 B

AWAHk4oP…CQoD641W Aa6RSnbq…vQge9Toq APKJumD5…qGY3sKoK AVk6Fshi…gsQzvctJ Ae2PMzTB…4fq3tk49

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.

2.555 × 10⁹⁶(97-digit number)

25550392742613684320…46835994659004707840

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

2.555 × 10⁹⁶(97-digit number)

25550392742613684320…46835994659004707839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.555 × 10⁹⁶(97-digit number)

25550392742613684320…46835994659004707841

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

5.110 × 10⁹⁶(97-digit number)

51100785485227368641…93671989318009415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.110 × 10⁹⁶(97-digit number)

51100785485227368641…93671989318009415681

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

1.022 × 10⁹⁷(98-digit number)

10220157097045473728…87343978636018831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.022 × 10⁹⁷(98-digit number)

10220157097045473728…87343978636018831361

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

2.044 × 10⁹⁷(98-digit number)

20440314194090947456…74687957272037662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.044 × 10⁹⁷(98-digit number)

20440314194090947456…74687957272037662721

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

4.088 × 10⁹⁷(98-digit number)

40880628388181894913…49375914544075325439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.088 × 10⁹⁷(98-digit number)

40880628388181894913…49375914544075325441

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

8.176 × 10⁹⁷(98-digit number)

81761256776363789826…98751829088150650879

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 1535785

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 c20c79a893bbb21c339e46bd3e7a9a3f3a9757ae8eecf66e1b871bc5c2635142

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 #1,535,785 on Chainz ↗

Block #1,535,785

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