Block #475,955

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 1:02:55 PM · Difficulty 10.4663 · 6,341,116 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

37d82c18ccc7cbb8bc97387a5527bc26c900f1dd560bc968cc08d867da9725cf

View on Chainz ↗

Height

#475,955

Difficulty

10.466296

Transactions

Size

884 B

Version

Bits

0a775f26

Nonce

223,874,571

Timestamp

4/5/2014, 1:02:55 PM

Confirmations

6,341,116

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f0f7717c2938beee920bbd6ebd1f74c72ace12840d3cf1a41a9f45acd90f3c3d

Transactions (4)

Coinbased1327f863d59a0…99dd079b3c5862

1 in → 1 out9.1400 XPM116 B

AbwWkWZt…kawDhufa

deaa92e31d483c…cec2a0fe70db44

1 in → 2 out5.0982 XPM226 B

AcMNnCDo…btimwL4a Ae3GMZeu…HB2n7Kho

3166be57ca61c5…f4c01b86160e80

1 in → 2 out3.0491 XPM225 B

AMWhfZow…EH5vsb34 AXpCMw15…Gcoyyqf5

abbf41b4988332…c5da6f7fc15839

1 in → 2 out1.6081 XPM225 B

APCza2xF…NYW1bK7F AeEeL76u…SxsTshMM

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.

2.525 × 10⁹⁸(99-digit number)

25253352807216733944…07936315742203791199

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

2.525 × 10⁹⁸(99-digit number)

25253352807216733944…07936315742203791199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.525 × 10⁹⁸(99-digit number)

25253352807216733944…07936315742203791201

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

5.050 × 10⁹⁸(99-digit number)

50506705614433467889…15872631484407582399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.050 × 10⁹⁸(99-digit number)

50506705614433467889…15872631484407582401

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

1.010 × 10⁹⁹(100-digit number)

10101341122886693577…31745262968815164799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.010 × 10⁹⁹(100-digit number)

10101341122886693577…31745262968815164801

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

2.020 × 10⁹⁹(100-digit number)

20202682245773387155…63490525937630329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.020 × 10⁹⁹(100-digit number)

20202682245773387155…63490525937630329601

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

4.040 × 10⁹⁹(100-digit number)

40405364491546774311…26981051875260659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.040 × 10⁹⁹(100-digit number)

40405364491546774311…26981051875260659201

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 #475,955

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