Block #278,708

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 2:22:47 AM · Difficulty 9.9696 · 6,525,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6be6392fa8a5cee159ae4791e86f898748b930cb355fb918fbc6e05e417e3760

View on Chainz ↗

Height

#278,708

Difficulty

9.969644

Transactions

Size

3.31 KB

Version

Bits

09f83a96

Nonce

4,517

Timestamp

11/28/2013, 2:22:47 AM

Confirmations

6,525,054

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

d3758e28d41bba4b3d1b40d871586520cd5e5acd74ae1e8bcc8f2c031c9486ba

Transactions (4)

Coinbase0cc00a50c93a9f…cf40837e21880b

1 in → 2 out10.1018 XPM142 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

68b0d88e6e6092…6be57f2bbace1c

2 in → 2 out1038.8310 XPM373 B

Ae1eZMqn…jsFquTAJ ASJ4P2Zy…ZfKjQdez

41f830260bed37…275c18e50111ef

3 in → 2 out396.5052 XPM521 B

AUCRa3Eb…o4UcpEdw APwgxK67…D8EZ5Qev

e458ff78fa5a83…fa3c6b11162ae0

15 in → 1 out4.9500 XPM2.21 KB

AWUFS5Ap…ypAacZ2u

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.

6.405 × 10¹⁰⁴(105-digit number)

64054811002049670885…59407626096785848319

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

6.405 × 10¹⁰⁴(105-digit number)

64054811002049670885…59407626096785848319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.405 × 10¹⁰⁴(105-digit number)

64054811002049670885…59407626096785848321

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

1.281 × 10¹⁰⁵(106-digit number)

12810962200409934177…18815252193571696639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.281 × 10¹⁰⁵(106-digit number)

12810962200409934177…18815252193571696641

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

2.562 × 10¹⁰⁵(106-digit number)

25621924400819868354…37630504387143393279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.562 × 10¹⁰⁵(106-digit number)

25621924400819868354…37630504387143393281

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

5.124 × 10¹⁰⁵(106-digit number)

51243848801639736708…75261008774286786559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.124 × 10¹⁰⁵(106-digit number)

51243848801639736708…75261008774286786561

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

1.024 × 10¹⁰⁶(107-digit number)

10248769760327947341…50522017548573573119

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