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Block #1,430,066

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2016, 5:59:33 AM · Difficulty 10.7483 · 5,412,773 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fbbdbbcb8c38a3347b13c873175fa974d19ecd928f5027399ea9bec1817fdcaf

View on Chainz ↗

Height

#1,430,066

Difficulty

10.748270

Transactions

Size

663 B

Version

Bits

0abf8e9a

Nonce

519,707,613

Timestamp

1/27/2016, 5:59:33 AM

Confirmations

5,412,773

Merkle Root

d57c22de76c903f522357f3f69a7365d8ebdb69c568c474fdf874665db395d7e

Transactions (2)

Coinbase287b9fcbc39a30…74750b7443dbd9

1 in → 1 out8.6500 XPM109 B

AYWrbWuV…wfrsn7dZ

35932830e0b9a9…faa30fb516a51e

1 in → 9 out188.9074 XPM464 B

AT1oTbdU…zkY2kuSH AHnsymnt…5DFYZsFP APdEknMG…7DffDjeh AW6zRY4z…ELnj21DS AKJWP64b…xFn4ggkM

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.

3.882 × 10⁹⁵(96-digit number)

38825682294235741036…01109423050166113920

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

3.882 × 10⁹⁵(96-digit number)

38825682294235741036…01109423050166113919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.882 × 10⁹⁵(96-digit number)

38825682294235741036…01109423050166113921

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

7.765 × 10⁹⁵(96-digit number)

77651364588471482072…02218846100332227839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.765 × 10⁹⁵(96-digit number)

77651364588471482072…02218846100332227841

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

1.553 × 10⁹⁶(97-digit number)

15530272917694296414…04437692200664455679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.553 × 10⁹⁶(97-digit number)

15530272917694296414…04437692200664455681

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

3.106 × 10⁹⁶(97-digit number)

31060545835388592828…08875384401328911359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.106 × 10⁹⁶(97-digit number)

31060545835388592828…08875384401328911361

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

6.212 × 10⁹⁶(97-digit number)

62121091670777185657…17750768802657822719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.212 × 10⁹⁶(97-digit number)

62121091670777185657…17750768802657822721

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 1430066

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 fbbdbbcb8c38a3347b13c873175fa974d19ecd928f5027399ea9bec1817fdcaf

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 #1,430,066 on Chainz ↗

Block #1,430,066

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