Home/Chain Registry/Block #2,137,821

Block #2,137,821

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/30/2017, 9:05:17 AM · Difficulty 10.8862 · 4,704,147 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc48417aed59222308afdbfa202dcdb918ea6294dd9143e4c16fd3cfb2185361

View on Chainz ↗

Height

#2,137,821

Difficulty

10.886207

Transactions

Size

1.43 KB

Version

Bits

0ae2de7c

Nonce

963,316,399

Timestamp

5/30/2017, 9:05:17 AM

Confirmations

4,704,147

Merkle Root

b40c7ac7307488dedca5183af525e1188d2190b7493146c818e93e335d2e7f99

Transactions (4)

Coinbasef5ca7098f73361…725a6f4bdbc579

1 in → 1 out8.4500 XPM109 B

AQ4PNG68…76TYfYWh

9765157b34659b…c47cc8aa0b5502

1 in → 2 out83239.5075 XPM226 B

AYuK1g5e…gkTPwDbz ARTj8R2D…JpT6ztpq

84ed512879fdaa…3334ee19ab455f

5 in → 2 out39.8425 XPM818 B

ATRTL965…9yC2qSSB Ad13QTN4…ddfdRmC1

0240eca55950ef…81f3b8a6251308

1 in → 2 out30780.6646 XPM226 B

AYuK1g5e…gkTPwDbz ALQzDEVB…hmg1zRfe

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.

1.116 × 10⁹²(93-digit number)

11162132049275053522…15683465260740083520

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

1.116 × 10⁹²(93-digit number)

11162132049275053522…15683465260740083519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.116 × 10⁹²(93-digit number)

11162132049275053522…15683465260740083521

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

2.232 × 10⁹²(93-digit number)

22324264098550107045…31366930521480167039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.232 × 10⁹²(93-digit number)

22324264098550107045…31366930521480167041

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

4.464 × 10⁹²(93-digit number)

44648528197100214090…62733861042960334079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.464 × 10⁹²(93-digit number)

44648528197100214090…62733861042960334081

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

8.929 × 10⁹²(93-digit number)

89297056394200428180…25467722085920668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.929 × 10⁹²(93-digit number)

89297056394200428180…25467722085920668161

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

1.785 × 10⁹³(94-digit number)

17859411278840085636…50935444171841336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.785 × 10⁹³(94-digit number)

17859411278840085636…50935444171841336321

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

3.571 × 10⁹³(94-digit number)

35718822557680171272…01870888343682672639

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 2137821

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 bc48417aed59222308afdbfa202dcdb918ea6294dd9143e4c16fd3cfb2185361

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 #2,137,821 on Chainz ↗

Block #2,137,821

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