Block #277,241

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 12:09:24 PM · Difficulty 9.9657 · 6,521,678 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a1b4777d760d8adcae5a2553e6da2d0d7f6d60c3ee4d0c11fa669d728b8ea48

View on Chainz ↗

Height

#277,241

Difficulty

9.965656

Transactions

Size

6.60 KB

Version

Bits

09f7353a

Nonce

2,200

Timestamp

11/27/2013, 12:09:24 PM

Confirmations

6,521,678

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

a36b08a0da655b06ba04fba62b83b002a8f9a52bae7e92956dea4a257e937041

Transactions (3)

Coinbaseba37459c176632…ef64e243b1408c

1 in → 2 out10.1300 XPM142 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

2375a384128086…743fbf32360a68

1 in → 2 out378.4495 XPM227 B

AK13uBcs…sBcaJax5 AUY1jqV9…TteZhnVN

c22fe2909d4c49…424dc34d507f24

42 in → 2 out13.7968 XPM6.14 KB

Af51Vnsk…Bx6gKoY4 ANtErSBW…2WYbje8z

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.

3.984 × 10¹⁰³(104-digit number)

39842683163495601518…09279611822913279039

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

3.984 × 10¹⁰³(104-digit number)

39842683163495601518…09279611822913279039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.984 × 10¹⁰³(104-digit number)

39842683163495601518…09279611822913279041

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

7.968 × 10¹⁰³(104-digit number)

79685366326991203036…18559223645826558079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.968 × 10¹⁰³(104-digit number)

79685366326991203036…18559223645826558081

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

1.593 × 10¹⁰⁴(105-digit number)

15937073265398240607…37118447291653116159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.593 × 10¹⁰⁴(105-digit number)

15937073265398240607…37118447291653116161

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

3.187 × 10¹⁰⁴(105-digit number)

31874146530796481214…74236894583306232319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.187 × 10¹⁰⁴(105-digit number)

31874146530796481214…74236894583306232321

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

6.374 × 10¹⁰⁴(105-digit number)

63748293061592962429…48473789166612464639

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