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Block #328,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 8:41:31 AM · Difficulty 10.1653 · 6,497,057 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a04d0d72e29183a5ef0bb1a677f9d511607c8165fd2444eb866688808d43d236

View on Chainz ↗

Height

#328,522

Difficulty

10.165271

Transactions

Size

4.04 KB

Version

Bits

0a2a4f2b

Nonce

109,942

Timestamp

12/25/2013, 8:41:31 AM

Confirmations

6,497,057

Merkle Root

aca543b739bf364682b09bc897441a2a431b43d287b5e4d0293c73824567f053

Transactions (2)

Coinbase031afa662e734a…34b12e30c622e1

1 in → 1 out9.7000 XPM110 B

AeKNrjNj…1NEq95Ta

cdb42d333d3b3d…2a974f2bdaa8da

26 in → 2 out8.3258 XPM3.84 KB

AVDHvpNx…UKXcnUY6 AXWMbncY…t5iChZYt

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.

1.845 × 10¹⁰⁰(101-digit number)

18451133987487770211…24817590387507509760

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

1.845 × 10¹⁰⁰(101-digit number)

18451133987487770211…24817590387507509759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.845 × 10¹⁰⁰(101-digit number)

18451133987487770211…24817590387507509761

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

3.690 × 10¹⁰⁰(101-digit number)

36902267974975540423…49635180775015019519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.690 × 10¹⁰⁰(101-digit number)

36902267974975540423…49635180775015019521

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

7.380 × 10¹⁰⁰(101-digit number)

73804535949951080846…99270361550030039039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.380 × 10¹⁰⁰(101-digit number)

73804535949951080846…99270361550030039041

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

1.476 × 10¹⁰¹(102-digit number)

14760907189990216169…98540723100060078079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.476 × 10¹⁰¹(102-digit number)

14760907189990216169…98540723100060078081

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

2.952 × 10¹⁰¹(102-digit number)

29521814379980432338…97081446200120156159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.952 × 10¹⁰¹(102-digit number)

29521814379980432338…97081446200120156161

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 328522

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 a04d0d72e29183a5ef0bb1a677f9d511607c8165fd2444eb866688808d43d236

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 #328,522 on Chainz ↗

Block #328,522

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