Block #357,720

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 2:36:15 PM · Difficulty 10.3860 · 6,460,139 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de238d5dddefccf4606bdfd05fa7f7c4d49e1a8dacc4b44ef960db764b43fafd

View on Chainz ↗

Height

#357,720

Difficulty

10.386006

Transactions

Size

1.08 KB

Version

Bits

0a62d14a

Nonce

201,086

Timestamp

1/13/2014, 2:36:15 PM

Confirmations

6,460,139

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9ba58e66bda1d2bfa33e534834afa75f666fc0ffcb9872d526ea963dd6bd640d

Transactions (5)

Coinbase0b61811b67e112…8219815f75090e

1 in → 1 out9.3000 XPM116 B

AbwWkWZt…kawDhufa

d3b8b4653aba7e…74748387bfb2a3

1 in → 2 out4.1076 XPM227 B

Aedwg9MC…K9NuQHM2 AHFfqLx1…cH63vh23

e2b119e06560df…d9c2805db19264

1 in → 2 out3.2420 XPM225 B

ANjE4rRU…gZ9FpSTJ AQagvnZU…2XRDKWPG

88a0b0509182a1…4dd3df30d6ec16

1 in → 2 out2.1764 XPM226 B

AV6h5nyy…TJ6sXzyW AMb3SMUy…N6MtixvT

f3a2bda0a30beb…2c76188bb63a99

1 in → 2 out4.0661 XPM227 B

AajzSvte…V7BMBiST Acn3iLqr…mU5Zae5Q

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.

2.593 × 10⁹³(94-digit number)

25936333647095112726…49505326478782113119

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

2.593 × 10⁹³(94-digit number)

25936333647095112726…49505326478782113119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.593 × 10⁹³(94-digit number)

25936333647095112726…49505326478782113121

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

5.187 × 10⁹³(94-digit number)

51872667294190225453…99010652957564226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.187 × 10⁹³(94-digit number)

51872667294190225453…99010652957564226241

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

1.037 × 10⁹⁴(95-digit number)

10374533458838045090…98021305915128452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.037 × 10⁹⁴(95-digit number)

10374533458838045090…98021305915128452481

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

2.074 × 10⁹⁴(95-digit number)

20749066917676090181…96042611830256904959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.074 × 10⁹⁴(95-digit number)

20749066917676090181…96042611830256904961

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

4.149 × 10⁹⁴(95-digit number)

41498133835352180362…92085223660513809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.149 × 10⁹⁴(95-digit number)

41498133835352180362…92085223660513809921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #357,720

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