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Block #2,653,055

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 2:21:28 AM · Difficulty 11.7406 · 4,180,462 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2ba5dc0e15853c0fc2153b0affa24e7996f98cb7bfb3412b0d6d8e888863307

View on Chainz ↗

Height

#2,653,055

Difficulty

11.740649

Transactions

Size

576 B

Version

Bits

0bbd9b2e

Nonce

2,102,782,219

Timestamp

5/8/2018, 2:21:28 AM

Confirmations

4,180,462

Merkle Root

258fac3344e03bcae8d71a6e74068c2974cd54c1f9757bace815566cc5613364

Transactions (2)

Coinbasea5dad4e10b5528…91bd0c652cf5b2

1 in → 1 out7.2500 XPM110 B

Adqah8zh…1WwoHJ9t

4583cc1a86052f…491001534888a5

2 in → 2 out4.3515 XPM374 B

ALFCjDjB…XEfXtzaq AbzVivCR…AGJbSBdK

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.

5.625 × 10⁹⁹(100-digit number)

56253177152390710553…41756808804522393600

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

5.625 × 10⁹⁹(100-digit number)

56253177152390710553…41756808804522393599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.625 × 10⁹⁹(100-digit number)

56253177152390710553…41756808804522393601

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

1.125 × 10¹⁰⁰(101-digit number)

11250635430478142110…83513617609044787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.125 × 10¹⁰⁰(101-digit number)

11250635430478142110…83513617609044787201

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

2.250 × 10¹⁰⁰(101-digit number)

22501270860956284221…67027235218089574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.250 × 10¹⁰⁰(101-digit number)

22501270860956284221…67027235218089574401

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

4.500 × 10¹⁰⁰(101-digit number)

45002541721912568443…34054470436179148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.500 × 10¹⁰⁰(101-digit number)

45002541721912568443…34054470436179148801

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

9.000 × 10¹⁰⁰(101-digit number)

90005083443825136886…68108940872358297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.000 × 10¹⁰⁰(101-digit number)

90005083443825136886…68108940872358297601

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

1.800 × 10¹⁰¹(102-digit number)

18001016688765027377…36217881744716595199

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 2653055

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 d2ba5dc0e15853c0fc2153b0affa24e7996f98cb7bfb3412b0d6d8e888863307

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 #2,653,055 on Chainz ↗

Block #2,653,055

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