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Block #267,340

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 5:12:51 AM · Difficulty 9.9591 · 6,523,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0674e89474a76f56527a01fe32a8bcfdaeeaab88d8ca2ee06ad80ece3ddd19d

View on Chainz ↗

Height

#267,340

Difficulty

9.959051

Transactions

Size

719 B

Version

Bits

09f58463

Nonce

153,533

Timestamp

11/21/2013, 5:12:51 AM

Confirmations

6,523,750

Merkle Root

5deeb748169d3b9785a1e4f2b0c2ba9e92d5a35de74544980c6ff45328295229

Transactions (2)

Coinbase5449c7b8d0ed70…0d3be8b8de1cb2

1 in → 1 out10.0800 XPM109 B

Adri1peA…DAdav5HF

650bc00798d976…efa5a7cfb2a206

3 in → 2 out166.2434 XPM520 B

AXWVJT6d…KisJkErQ Aeu7hLiG…LDavw3ya

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.

8.602 × 10⁹⁵(96-digit number)

86024271454260692661…45450565964672483520

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

8.602 × 10⁹⁵(96-digit number)

86024271454260692661…45450565964672483519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.602 × 10⁹⁵(96-digit number)

86024271454260692661…45450565964672483521

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

1.720 × 10⁹⁶(97-digit number)

17204854290852138532…90901131929344967039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.720 × 10⁹⁶(97-digit number)

17204854290852138532…90901131929344967041

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

3.440 × 10⁹⁶(97-digit number)

34409708581704277064…81802263858689934079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.440 × 10⁹⁶(97-digit number)

34409708581704277064…81802263858689934081

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

6.881 × 10⁹⁶(97-digit number)

68819417163408554129…63604527717379868159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.881 × 10⁹⁶(97-digit number)

68819417163408554129…63604527717379868161

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

1.376 × 10⁹⁷(98-digit number)

13763883432681710825…27209055434759736319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.376 × 10⁹⁷(98-digit number)

13763883432681710825…27209055434759736321

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 267340

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 c0674e89474a76f56527a01fe32a8bcfdaeeaab88d8ca2ee06ad80ece3ddd19d

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 #267,340 on Chainz ↗