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Block #2,633,475

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 11:15:07 AM · Difficulty 11.1927 · 4,198,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1aee09334e55e2ed3929c7a148c7670ab3f77f37e379162391dfcb5e986cdca

View on Chainz ↗

Height

#2,633,475

Difficulty

11.192685

Transactions

Size

1.00 KB

Version

Bits

0b3153c9

Nonce

727,250,269

Timestamp

4/28/2018, 11:15:07 AM

Confirmations

4,198,112

Merkle Root

4c547926626dde59fc856ca8c663859e915536e946e06f2202996ead4be9e474

Transactions (3)

Coinbase2467af6ff5c81d…b3fdadfccef085

1 in → 1 out7.9900 XPM110 B

ASVt69e7…UZAAuLVC

80a7558ef03623…12f725c53a7088

2 in → 2 out15.9700 XPM306 B

AHSWpUrB…aKSHiDiv AS8ZMJ7r…hJtnDVmA

a9d570ac342fd3…894c3b338d0882

3 in → 2 out10.0100 XPM522 B

AVyZAwA1…XGeDCq7T AHdq5Vdz…Z2ZSJw4F

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.

4.605 × 10⁹⁶(97-digit number)

46050741013227047907…29105396039496622080

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

4.605 × 10⁹⁶(97-digit number)

46050741013227047907…29105396039496622079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.605 × 10⁹⁶(97-digit number)

46050741013227047907…29105396039496622081

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

9.210 × 10⁹⁶(97-digit number)

92101482026454095815…58210792078993244159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.210 × 10⁹⁶(97-digit number)

92101482026454095815…58210792078993244161

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

1.842 × 10⁹⁷(98-digit number)

18420296405290819163…16421584157986488319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.842 × 10⁹⁷(98-digit number)

18420296405290819163…16421584157986488321

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

3.684 × 10⁹⁷(98-digit number)

36840592810581638326…32843168315972976639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.684 × 10⁹⁷(98-digit number)

36840592810581638326…32843168315972976641

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

7.368 × 10⁹⁷(98-digit number)

73681185621163276652…65686336631945953279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.368 × 10⁹⁷(98-digit number)

73681185621163276652…65686336631945953281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.473 × 10⁹⁸(99-digit number)

14736237124232655330…31372673263891906559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2633475

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 f1aee09334e55e2ed3929c7a148c7670ab3f77f37e379162391dfcb5e986cdca

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 #2,633,475 on Chainz ↗

Block #2,633,475

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