Home/Chain Registry/Block #417,518

Block #417,518

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 5:55:16 AM · Difficulty 10.3901 · 6,425,755 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3799079336d93adccfc44890e1d33ac647261a3d505c169e9b4c0449bfd3736

View on Chainz ↗

Height

#417,518

Difficulty

10.390055

Transactions

Size

2.32 KB

Version

Bits

0a63daad

Nonce

557,985

Timestamp

2/24/2014, 5:55:16 AM

Confirmations

6,425,755

Merkle Root

71cd9eca728f8306fea72a39fcb1b07e47aa3651ae264bcd43c497d3207a5c86

Transactions (4)

Coinbase3311f5e7e805ef…1907fc6f6ec897

1 in → 25 out9.2800 XPM913 B

AGz9gyZW…bo8NYQpw AcuM7XiJ…5uND8Jce AapDs2MB…Ru6E3pCr AQFhQpUS…HmKbSyAx AMW1p9oT…2TzdaZxH

19ce147d2a05dc…a7b070ab696002

1 in → 2 out9.3200 XPM192 B

ARSEqb1P…jv1Wy9aq AJbq7Mk7…NKwRjJLP

9a80ad203da74d…1bb5ec029437e3

3 in → 10 out27.7700 XPM692 B

AYJqzDSV…rHuxyuhC AYBxxNcP…EyxWsFHb AKZsCWK8…ZTTZQMnu AUbuMqhM…Yi6edrK9 AeKNrjNj…1NEq95Ta

f86860d4e720a3…0d4c461506d5a1

3 in → 1 out3.0126 XPM487 B

ANNpb1aN…sthRhUwd

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.

1.080 × 10⁹⁶(97-digit number)

10801422514549882675…57285358042718459040

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

1.080 × 10⁹⁶(97-digit number)

10801422514549882675…57285358042718459039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.080 × 10⁹⁶(97-digit number)

10801422514549882675…57285358042718459041

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

2.160 × 10⁹⁶(97-digit number)

21602845029099765350…14570716085436918079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.160 × 10⁹⁶(97-digit number)

21602845029099765350…14570716085436918081

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

4.320 × 10⁹⁶(97-digit number)

43205690058199530700…29141432170873836159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.320 × 10⁹⁶(97-digit number)

43205690058199530700…29141432170873836161

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

8.641 × 10⁹⁶(97-digit number)

86411380116399061400…58282864341747672319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.641 × 10⁹⁶(97-digit number)

86411380116399061400…58282864341747672321

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

1.728 × 10⁹⁷(98-digit number)

17282276023279812280…16565728683495344639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.728 × 10⁹⁷(98-digit number)

17282276023279812280…16565728683495344641

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 417518

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 b3799079336d93adccfc44890e1d33ac647261a3d505c169e9b4c0449bfd3736

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 #417,518 on Chainz ↗

Block #417,518

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