Block #277,842

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 5:55:07 PM · Difficulty 9.9674 · 6,538,124 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

495d077955e3e746603d7e70dbdd2d295e95cd5e30a965b002b9de880756d597

View on Chainz ↗

Height

#277,842

Difficulty

9.967374

Transactions

Size

1.11 KB

Version

Bits

09f7a5cd

Nonce

43,635

Timestamp

11/27/2013, 5:55:07 PM

Confirmations

6,538,124

Mined by

⛏️ P2SHAQWESWsF3kkvM7LLE7rV3u4NU8K9jDDzgA

Merkle Root

c15e2124ceaefb54b9fb2b8c0842eaab0eff01fbbf305f4014106259722626ef

Transactions (4)

Coinbase55a9963851b2c7…2aaa9b41b5eec4

1 in → 1 out10.0800 XPM109 B

AQWESWsF…K9jDDzgA

931d4fd2ff7a8e…586af2c39ebd71

3 in → 1 out1197.5000 XPM488 B

AZze4xmU…TKWbkzD4

25fe5141ce615c…a4fbb77cde78af

1 in → 2 out1.9023 XPM225 B

AcpEdeH6…xRdYV1cE AZtFPifF…DaugVair

17a52494d62052…ede4bec99a9eff

1 in → 2 out1.9512 XPM227 B

AThJTttV…tg219FUf AJJCSeuJ…LDet4AK1

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.

1.910 × 10⁹⁵(96-digit number)

19109123416857384412…85492074865347348479

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

1.910 × 10⁹⁵(96-digit number)

19109123416857384412…85492074865347348479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.910 × 10⁹⁵(96-digit number)

19109123416857384412…85492074865347348481

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

3.821 × 10⁹⁵(96-digit number)

38218246833714768824…70984149730694696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.821 × 10⁹⁵(96-digit number)

38218246833714768824…70984149730694696961

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

7.643 × 10⁹⁵(96-digit number)

76436493667429537648…41968299461389393919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.643 × 10⁹⁵(96-digit number)

76436493667429537648…41968299461389393921

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

1.528 × 10⁹⁶(97-digit number)

15287298733485907529…83936598922778787839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.528 × 10⁹⁶(97-digit number)

15287298733485907529…83936598922778787841

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

3.057 × 10⁹⁶(97-digit number)

30574597466971815059…67873197845557575679

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 #277,842

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