Block #455,108

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 9:05:47 AM · Difficulty 10.4036 · 6,354,860 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33d81131fb3d806e4d30c3ab3ad06a73001caff13ca8cf1a87c249acb86661ab

View on Chainz ↗

Height

#455,108

Difficulty

10.403576

Transactions

Size

2.17 KB

Version

Bits

0a6750c5

Nonce

13,914

Timestamp

3/22/2014, 9:05:47 AM

Confirmations

6,354,860

Mined by

⛏️ aS-R`0AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

359cf06b4f3e4570f318b4f49807838040c9473c9d64deb3e8b4e08e78a9bd66

Transactions (4)

Coinbase48838bcb2fd0c8…5dfd65424202dc

1 in → 22 out9.2200 XPM811 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq ATv3Pbhq…4aHz5j1G

48af0d91569de6…11e246f17e9cd6

4 in → 12 out37.1400 XPM874 B

AeKNrjNj…1NEq95Ta AUsZtomw…72QacKG5 AP5i7QoC…HmBrELxR AXW5oy9W…fVjVrfCH AbegGsha…RYQxrpFP

b91747f5a691ec…cdb0f2950ea49a

1 in → 2 out6.1872 XPM226 B

ASizZgzZ…3wDzLpyL AFv7ik1Q…GXfNA16m

aef489aaad36ff…4326e3e9275afd

1 in → 2 out5.1636 XPM225 B

AP2GxFDi…MZQBdSYt AWeWcW4s…Y7AUCxqk

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.

1.032 × 10⁹⁴(95-digit number)

10329101747285205861…18734880828638548079

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

1.032 × 10⁹⁴(95-digit number)

10329101747285205861…18734880828638548079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.032 × 10⁹⁴(95-digit number)

10329101747285205861…18734880828638548081

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

2.065 × 10⁹⁴(95-digit number)

20658203494570411723…37469761657277096159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.065 × 10⁹⁴(95-digit number)

20658203494570411723…37469761657277096161

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

4.131 × 10⁹⁴(95-digit number)

41316406989140823446…74939523314554192319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.131 × 10⁹⁴(95-digit number)

41316406989140823446…74939523314554192321

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

8.263 × 10⁹⁴(95-digit number)

82632813978281646892…49879046629108384639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.263 × 10⁹⁴(95-digit number)

82632813978281646892…49879046629108384641

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

1.652 × 10⁹⁵(96-digit number)

16526562795656329378…99758093258216769279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.652 × 10⁹⁵(96-digit number)

16526562795656329378…99758093258216769281

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 #455,108

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