Block #281,178

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 10:36:06 PM · Difficulty 9.9764 · 6,519,519 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d98ebf9f4db753fca18e20f2289cd610e935ceac342f329e935256f89ccb13df

View on Chainz ↗

Height

#281,178

Difficulty

9.976409

Transactions

Size

2.32 KB

Version

Bits

09f9f5f3

Nonce

30,938

Timestamp

11/28/2013, 10:36:06 PM

Confirmations

6,519,519

Mined by

⛏️ ZJaRhAQL2NQp7EfJCRP9A7ACYWDM7EujaCPriAU

Merkle Root

66408a1e4a76d7596d1cbf494a67c8a5ff427bbfb2976e047f04ca8910ced501

Transactions (4)

Coinbasebfe83c3cc8ada0…d87cf3190b04b8

1 in → 22 out10.0300 XPM811 B

AQL2NQp7…jaCPriAU ANuKx9Ke…wm7nrBRq AbtgNzNb…9Atvu81w ANN5ySFG…qocMaEhA AaN3X4nJ…7DX2KLvh

c8919f169d48c6…a34ad1ff4d9476

5 in → 13 out50.2800 XPM1023 B

AdJXXMWa…yv1pUHFk ASyA6WF3…YdRDbU43 AYpANtX5…cpBRh2BL ASWp6454…JFPEKgqq AKL6bdQp…hNjj8m2T

f2cd0e9c82c14e…f64fd8dadd2d9e

1 in → 2 out9.0149 XPM226 B

AMLHwB9n…DsCYsu7f AR4ecMEH…X4W52fQT

c5ccb578026a4a…ef74ef7dfc383d

1 in → 2 out6.9837 XPM225 B

AQ3X2VZb…inCyY6Rn AdQPh5YX…pJkK23qT

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.

1.257 × 10⁹³(94-digit number)

12571822377943993643…09166918745458306239

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

1.257 × 10⁹³(94-digit number)

12571822377943993643…09166918745458306239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.257 × 10⁹³(94-digit number)

12571822377943993643…09166918745458306241

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

2.514 × 10⁹³(94-digit number)

25143644755887987286…18333837490916612479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.514 × 10⁹³(94-digit number)

25143644755887987286…18333837490916612481

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

5.028 × 10⁹³(94-digit number)

50287289511775974573…36667674981833224959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.028 × 10⁹³(94-digit number)

50287289511775974573…36667674981833224961

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

1.005 × 10⁹⁴(95-digit number)

10057457902355194914…73335349963666449919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.005 × 10⁹⁴(95-digit number)

10057457902355194914…73335349963666449921

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

2.011 × 10⁹⁴(95-digit number)

20114915804710389829…46670699927332899839

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