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Block #551,742

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/19/2014, 12:49:53 AM · Difficulty 10.9624 · 6,262,187 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

153da2ab4e82ae750f59f4ce06799cf252b8f8994085ac18e8ad112b66fc87d2

View on Chainz ↗

Height

#551,742

Difficulty

10.962364

Transactions

Size

244 B

Version

Bits

0af65d79

Nonce

95,412,906

Timestamp

5/19/2014, 12:49:53 AM

Confirmations

6,262,187

Merkle Root

25d5caac3918ddab735d770c39a1b6a9826a3197c46b595f84a96535ab8634e9

Transactions (1)

Coinbase25d5caac3918dd…a96535ab8634e9

1 in → 2 out8.3100 XPM152 B

AV7NKdpo…AkUnvExY ALPu3s2c…EJXLjVFh

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.

1.624 × 10⁹⁸(99-digit number)

16249199740657966726…63332553098541756760

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

1.624 × 10⁹⁸(99-digit number)

16249199740657966726…63332553098541756759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.624 × 10⁹⁸(99-digit number)

16249199740657966726…63332553098541756761

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

3.249 × 10⁹⁸(99-digit number)

32498399481315933452…26665106197083513519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.249 × 10⁹⁸(99-digit number)

32498399481315933452…26665106197083513521

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

6.499 × 10⁹⁸(99-digit number)

64996798962631866905…53330212394167027039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.499 × 10⁹⁸(99-digit number)

64996798962631866905…53330212394167027041

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

1.299 × 10⁹⁹(100-digit number)

12999359792526373381…06660424788334054079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.299 × 10⁹⁹(100-digit number)

12999359792526373381…06660424788334054081

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

2.599 × 10⁹⁹(100-digit number)

25998719585052746762…13320849576668108159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.599 × 10⁹⁹(100-digit number)

25998719585052746762…13320849576668108161

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 551742

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 153da2ab4e82ae750f59f4ce06799cf252b8f8994085ac18e8ad112b66fc87d2

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 #551,742 on Chainz ↗

Block #551,742

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