Home/Chain Registry/Block #414,909

Block #414,909

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/22/2014, 8:47:15 AM · Difficulty 10.3996 · 6,411,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

61932d5594e82c73780c1468c4b3b2a4de1300d1534f1d96da62a4227716634f

View on Chainz ↗

Height

#414,909

Difficulty

10.399635

Transactions

Size

834 B

Version

Bits

0a664e81

Nonce

148,862

Timestamp

2/22/2014, 8:47:15 AM

Confirmations

6,411,360

Merkle Root

bb52640ddf439478f208d85d555686cc393201fd62f674111ad044be671e6d41

Transactions (1)

Coinbasebb52640ddf4394…d044be671e6d41

1 in → 20 out9.2266 XPM743 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

2.788 × 10⁹⁶(97-digit number)

27887395898139313228…33616623533660456960

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

2.788 × 10⁹⁶(97-digit number)

27887395898139313228…33616623533660456959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.788 × 10⁹⁶(97-digit number)

27887395898139313228…33616623533660456961

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

5.577 × 10⁹⁶(97-digit number)

55774791796278626456…67233247067320913919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.577 × 10⁹⁶(97-digit number)

55774791796278626456…67233247067320913921

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

1.115 × 10⁹⁷(98-digit number)

11154958359255725291…34466494134641827839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.115 × 10⁹⁷(98-digit number)

11154958359255725291…34466494134641827841

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

2.230 × 10⁹⁷(98-digit number)

22309916718511450582…68932988269283655679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.230 × 10⁹⁷(98-digit number)

22309916718511450582…68932988269283655681

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

4.461 × 10⁹⁷(98-digit number)

44619833437022901165…37865976538567311359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.461 × 10⁹⁷(98-digit number)

44619833437022901165…37865976538567311361

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 414909

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 61932d5594e82c73780c1468c4b3b2a4de1300d1534f1d96da62a4227716634f

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 #414,909 on Chainz ↗

Block #414,909

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