Block #270,494

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 11:54:08 PM · Difficulty 9.9517 · 6,539,475 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

674007bb0c86304ae6aac67fc63bf12591d5aaef8a46d373f90675ff7c0634b6

View on Chainz ↗

Height

#270,494

Difficulty

9.951704

Transactions

Size

1.58 KB

Version

Bits

09f3a2e1

Nonce

65,787

Timestamp

11/23/2013, 11:54:08 PM

Confirmations

6,539,475

Mined by

⛏️ P2SHAbi1Q71oC7u2iALyeunNVA63YroL8uM1HN

Merkle Root

099b4c5f53026645d3d4ea9b8911a2eadbc5571209603498838761de9dcde795

Transactions (4)

Coinbase7d122e0e6bf16e…8b9c3da408f03e

1 in → 1 out10.1200 XPM109 B

Abi1Q71o…oL8uM1HN

a32ed202b5096d…c099c4bcc1f2d1

2 in → 2 out16.0681 XPM374 B

AV4iR27J…PpSaBXQD AN4KokSc…8oFYPA8o

09719688fc69f7…9c601729a43614

1 in → 2 out4.2300 XPM226 B

AWKhcKD1…AK1RJ4a3 AVkAdABx…uMBoJsm7

a8ed5aca68b026…0f6fb9ec053d09

5 in → 2 out10.0238 XPM821 B

AbCYrMXU…9oKvDFop AH4tDC6R…brtb8mnZ

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.

1.916 × 10⁹³(94-digit number)

19161073068642784814…42870862181012558019

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

1.916 × 10⁹³(94-digit number)

19161073068642784814…42870862181012558019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.916 × 10⁹³(94-digit number)

19161073068642784814…42870862181012558021

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

3.832 × 10⁹³(94-digit number)

38322146137285569629…85741724362025116039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.832 × 10⁹³(94-digit number)

38322146137285569629…85741724362025116041

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

7.664 × 10⁹³(94-digit number)

76644292274571139259…71483448724050232079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.664 × 10⁹³(94-digit number)

76644292274571139259…71483448724050232081

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

1.532 × 10⁹⁴(95-digit number)

15328858454914227851…42966897448100464159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.532 × 10⁹⁴(95-digit number)

15328858454914227851…42966897448100464161

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

3.065 × 10⁹⁴(95-digit number)

30657716909828455703…85933794896200928319

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Cross-reference on Chainz Explorer

Block #270,494

Cookie Preferences