Home/Chain Registry/Block #848,217

Block #848,217

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/10/2014, 10:22:18 PM · Difficulty 10.9717 · 5,994,717 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2bae90d2ca32304e95eea7a1bb9366bb91dd0891dc65c950388a80373f63a68

View on Chainz ↗

Height

#848,217

Difficulty

10.971663

Transactions

Size

800 B

Version

Bits

0af8beec

Nonce

1,544,006,562

Timestamp

12/10/2014, 10:22:18 PM

Confirmations

5,994,717

Merkle Root

05e46524a54a9b86f550f9c606e0056c0f04a3ab2d8e16f9dabca54e536c52c1

Transactions (3)

Coinbaseb7ff43350f08b2…f4ed38e789ed2d

1 in → 1 out8.3200 XPM110 B

AaLrNkzS…4G1T5RUU

602995ff2b86d7…e90315b9aae62a

1 in → 2 out0.1555 XPM226 B

ATCLsETb…rG7wBvqi ANM4U7me…KbZGZoFB

e32fe2faafd650…9beb86043af1b3

2 in → 2 out0.0283 XPM374 B

AP4ghXg5…EdeWFycA APMjaCtN…oDtkSvHn

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.

2.121 × 10⁹⁴(95-digit number)

21210058847755537692…19250031492852534400

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

2.121 × 10⁹⁴(95-digit number)

21210058847755537692…19250031492852534399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.121 × 10⁹⁴(95-digit number)

21210058847755537692…19250031492852534401

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

4.242 × 10⁹⁴(95-digit number)

42420117695511075385…38500062985705068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.242 × 10⁹⁴(95-digit number)

42420117695511075385…38500062985705068801

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

8.484 × 10⁹⁴(95-digit number)

84840235391022150771…77000125971410137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.484 × 10⁹⁴(95-digit number)

84840235391022150771…77000125971410137601

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

1.696 × 10⁹⁵(96-digit number)

16968047078204430154…54000251942820275199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.696 × 10⁹⁵(96-digit number)

16968047078204430154…54000251942820275201

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

3.393 × 10⁹⁵(96-digit number)

33936094156408860308…08000503885640550399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.393 × 10⁹⁵(96-digit number)

33936094156408860308…08000503885640550401

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

6.787 × 10⁹⁵(96-digit number)

67872188312817720616…16001007771281100799

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 848217

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 d2bae90d2ca32304e95eea7a1bb9366bb91dd0891dc65c950388a80373f63a68

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 #848,217 on Chainz ↗

Block #848,217

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