Block #278,741

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 2:43:17 AM · Difficulty 9.9697 · 6,518,090 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b25de7be568b1a2b9d8e9983fffa4290a475ffb7cb830f8255f1cacedf68757

View on Chainz ↗

Height

#278,741

Difficulty

9.969717

Transactions

Size

1.04 KB

Version

Bits

09f83f60

Nonce

101,779

Timestamp

11/28/2013, 2:43:17 AM

Confirmations

6,518,090

Mined by

⛏️ P2SHARJr4BLPkgUUudhUmU8Kfz1VLeJL2dBVRP

Merkle Root

6bc8d7a2190d98acdc50919ca9af0d694c1aeb249bedf41980df00c957a56461

Transactions (3)

Coinbase90619e526ca859…6b0ffd174626ec

1 in → 1 out10.0700 XPM109 B

ARJr4BLP…JL2dBVRP

c05104b1e252db…c69dd94fcc47ce

3 in → 2 out1.0103 XPM523 B

Aei3uULa…PXg7vrG7 AXG8RPKM…sDVv3onc

2c9841ffd88781…9fb72353bc7373

2 in → 1 out48.7700 XPM339 B

ARFBrkBo…FSjfnR8N

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.

1.023 × 10⁹³(94-digit number)

10237502985501888948…06706986988015696529

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

1.023 × 10⁹³(94-digit number)

10237502985501888948…06706986988015696529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.023 × 10⁹³(94-digit number)

10237502985501888948…06706986988015696531

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

2.047 × 10⁹³(94-digit number)

20475005971003777896…13413973976031393059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.047 × 10⁹³(94-digit number)

20475005971003777896…13413973976031393061

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

4.095 × 10⁹³(94-digit number)

40950011942007555793…26827947952062786119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.095 × 10⁹³(94-digit number)

40950011942007555793…26827947952062786121

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

8.190 × 10⁹³(94-digit number)

81900023884015111587…53655895904125572239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.190 × 10⁹³(94-digit number)

81900023884015111587…53655895904125572241

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

1.638 × 10⁹⁴(95-digit number)

16380004776803022317…07311791808251144479

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