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Block #2,634,779

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 12:38:27 AM · Difficulty 11.2691 · 4,195,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60f43aa34885adacab6774b53630230d801b7c967734f81cce5687cf761ce03d

View on Chainz ↗

Height

#2,634,779

Difficulty

11.269103

Transactions

Size

606 B

Version

Bits

0b44e3e7

Nonce

147,988,730

Timestamp

4/29/2018, 12:38:27 AM

Confirmations

4,195,807

Merkle Root

d29a7ef501c2b717fd01da3065a98580f88226c147182a5a71c2ec314565e813

Transactions (2)

Coinbase782bb2808f0398…950cdddcbfe420

1 in → 1 out7.8700 XPM110 B

AGcC7s2M…RMKeMCT7

6d2c978adc684b…8c38b07838825b

2 in → 3 out57.6557 XPM407 B

APi8C85f…Lg5MDiei APWHbUGD…2Sifwq6j ARznVePF…S7wvbB9s

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.

1.072 × 10⁹³(94-digit number)

10728748481686978329…85195291319544404480

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

1.072 × 10⁹³(94-digit number)

10728748481686978329…85195291319544404479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.072 × 10⁹³(94-digit number)

10728748481686978329…85195291319544404481

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

2.145 × 10⁹³(94-digit number)

21457496963373956659…70390582639088808959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.145 × 10⁹³(94-digit number)

21457496963373956659…70390582639088808961

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

4.291 × 10⁹³(94-digit number)

42914993926747913318…40781165278177617919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.291 × 10⁹³(94-digit number)

42914993926747913318…40781165278177617921

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

8.582 × 10⁹³(94-digit number)

85829987853495826637…81562330556355235839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.582 × 10⁹³(94-digit number)

85829987853495826637…81562330556355235841

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

1.716 × 10⁹⁴(95-digit number)

17165997570699165327…63124661112710471679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.716 × 10⁹⁴(95-digit number)

17165997570699165327…63124661112710471681

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

3.433 × 10⁹⁴(95-digit number)

34331995141398330655…26249322225420943359

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 2634779

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 60f43aa34885adacab6774b53630230d801b7c967734f81cce5687cf761ce03d

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 #2,634,779 on Chainz ↗

Block #2,634,779

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