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Block #270,274

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 7:57:31 PM · Difficulty 9.9519 · 6,572,845 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2af0d73bae2820b34d10e690dc355f3c0f7b35933f07577aee3982d00199f3ad

View on Chainz ↗

Height

#270,274

Difficulty

9.951875

Transactions

Size

2.75 KB

Version

Bits

09f3ae0d

Nonce

132,529

Timestamp

11/23/2013, 7:57:31 PM

Confirmations

6,572,845

Merkle Root

ad9dc7a96dee4fb5546ae91c88f93cc0425428639431952d3a6e4ab34c5da894

Transactions (2)

Coinbasef2fbfaec64319b…6c138f718107cb

1 in → 50 out10.0600 XPM1.72 KB

ATKK7iFz…wZm46KN1 AFqKfjez…qX9Ace3g ARcCgqrB…JAqh9Eqe ANmkKL2U…jPxj1Qs3 ARpndEmc…Hg792kEk

9c8da6dd8a7373…16fa3d1d2f8add

6 in → 2 out10.4083 XPM965 B

Aa2JA2Lk…R4Q3S5WK AaKMadth…3F92ZGqD

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.

5.852 × 10⁹³(94-digit number)

58523204450772629569…44051531552180058440

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

5.852 × 10⁹³(94-digit number)

58523204450772629569…44051531552180058439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.852 × 10⁹³(94-digit number)

58523204450772629569…44051531552180058441

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

1.170 × 10⁹⁴(95-digit number)

11704640890154525913…88103063104360116879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.170 × 10⁹⁴(95-digit number)

11704640890154525913…88103063104360116881

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

2.340 × 10⁹⁴(95-digit number)

23409281780309051827…76206126208720233759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.340 × 10⁹⁴(95-digit number)

23409281780309051827…76206126208720233761

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

4.681 × 10⁹⁴(95-digit number)

46818563560618103655…52412252417440467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.681 × 10⁹⁴(95-digit number)

46818563560618103655…52412252417440467521

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

9.363 × 10⁹⁴(95-digit number)

93637127121236207311…04824504834880935039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 270274

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 2af0d73bae2820b34d10e690dc355f3c0f7b35933f07577aee3982d00199f3ad

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 #270,274 on Chainz ↗

Block #270,274

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