Block #3,504,301

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2020, 7:35:59 PM · Difficulty 10.9310 · 3,338,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64a3b42474df2b130bac1f2ccc3e413f670ad9ddad7dbdf6f73f7cbaaf976bc6

View on Chainz ↗

Height

#3,504,301

Difficulty

10.930996

Transactions

Size

22.00 KB

Version

Bits

0aee55ba

Nonce

1,170,663,864

Timestamp

1/7/2020, 7:35:59 PM

Confirmations

3,338,591

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

4a882ea4947baca7279ec3bf254d086375accae5c4cf3103db5fcc9d8315b943

Transactions (4)

Coinbase0e8d4592e3cfbf…46d124caba9b19

1 in → 1 out8.6000 XPM110 B

ASiq2qtK…VMhmk7yL

b89ac6923bd949…d12b796f94e840

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

59e307ad82cf85…c3de3535bb359d

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

91c717d3571e23…7ca8a2e130fa1b

50 in → 1 out5097.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

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.

8.396 × 10⁹⁵(96-digit number)

83963806116215669451…62637769809827263999

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

8.396 × 10⁹⁵(96-digit number)

83963806116215669451…62637769809827263999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.396 × 10⁹⁵(96-digit number)

83963806116215669451…62637769809827264001

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

1.679 × 10⁹⁶(97-digit number)

16792761223243133890…25275539619654527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.679 × 10⁹⁶(97-digit number)

16792761223243133890…25275539619654528001

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

3.358 × 10⁹⁶(97-digit number)

33585522446486267780…50551079239309055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.358 × 10⁹⁶(97-digit number)

33585522446486267780…50551079239309056001

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

6.717 × 10⁹⁶(97-digit number)

67171044892972535561…01102158478618111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.717 × 10⁹⁶(97-digit number)

67171044892972535561…01102158478618112001

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

1.343 × 10⁹⁷(98-digit number)

13434208978594507112…02204316957236223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.343 × 10⁹⁷(98-digit number)

13434208978594507112…02204316957236224001

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 #3,504,301

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