Home/Chain Registry/Block #2,653,134

Block #2,653,134

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 3:50:36 AM · Difficulty 11.7402 · 4,180,852 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97ae76d7df5a959eb816f22936f589fc0998b5206143df566f8bec77e5757a33

View on Chainz ↗

Height

#2,653,134

Difficulty

11.740176

Transactions

Size

426 B

Version

Bits

0bbd7c2f

Nonce

5,411,983

Timestamp

5/8/2018, 3:50:36 AM

Confirmations

4,180,852

Merkle Root

ecbbcccd238804b8b2d46b8dcbca3c12763fd6660fb8611101614bacaf695246

Transactions (2)

Coinbasec8ae24ae92e82e…1dfb8a3d2ca7c5

1 in → 1 out7.2500 XPM110 B

ANqeqKnH…vBrjvQTu

e9cc1b1af7ee02…f85659abf0a6af

1 in → 2 out1.1627 XPM226 B

AHmoHaoV…guxDRZ3w ANULSiJF…w2ZtDX9R

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.

6.896 × 10⁹⁴(95-digit number)

68965395540473170062…58412603923577797200

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

6.896 × 10⁹⁴(95-digit number)

68965395540473170062…58412603923577797199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.896 × 10⁹⁴(95-digit number)

68965395540473170062…58412603923577797201

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

1.379 × 10⁹⁵(96-digit number)

13793079108094634012…16825207847155594399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.379 × 10⁹⁵(96-digit number)

13793079108094634012…16825207847155594401

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

2.758 × 10⁹⁵(96-digit number)

27586158216189268025…33650415694311188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.758 × 10⁹⁵(96-digit number)

27586158216189268025…33650415694311188801

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

5.517 × 10⁹⁵(96-digit number)

55172316432378536050…67300831388622377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.517 × 10⁹⁵(96-digit number)

55172316432378536050…67300831388622377601

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

1.103 × 10⁹⁶(97-digit number)

11034463286475707210…34601662777244755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.103 × 10⁹⁶(97-digit number)

11034463286475707210…34601662777244755201

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

2.206 × 10⁹⁶(97-digit number)

22068926572951414420…69203325554489510399

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 2653134

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 97ae76d7df5a959eb816f22936f589fc0998b5206143df566f8bec77e5757a33

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 #2,653,134 on Chainz ↗

Block #2,653,134

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