Block #3,505,267

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2020, 12:07:28 PM · Difficulty 10.9306 · 3,334,783 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ded708d9d4e1b4c84e47b4fc4b6b856194f8fcde75d32d44e9ac1a821a925cf

View on Chainz ↗

Height

#3,505,267

Difficulty

10.930649

Transactions

Size

29.29 KB

Version

Bits

0aee3f0b

Nonce

63,051,924

Timestamp

1/8/2020, 12:07:28 PM

Confirmations

3,334,783

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

f399ed7c7f7ef97ab309279f598c5fb5bd657a003e6b97e4bdcda1f80d91ae6b

Transactions (5)

Coinbase37e47c19130391…374480831eff21

1 in → 1 out8.6800 XPM109 B

ASiq2qtK…VMhmk7yL

0f54fad67a6fa8…fec7d0b436d8f7

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

5d32eb9cbeddc6…f0a30bd538f6b7

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

299b4672323346…1657b457db27f5

50 in → 1 out199.9200 XPM7.28 KB

ALcTQaSP…1C5Yf2Zi

d37b558f296717…16bbc5538cc10c

50 in → 1 out5685.6800 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.

5.634 × 10⁹⁵(96-digit number)

56343926826073395364…85877455851247710719

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

5.634 × 10⁹⁵(96-digit number)

56343926826073395364…85877455851247710719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.634 × 10⁹⁵(96-digit number)

56343926826073395364…85877455851247710721

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

1.126 × 10⁹⁶(97-digit number)

11268785365214679072…71754911702495421439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.126 × 10⁹⁶(97-digit number)

11268785365214679072…71754911702495421441

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

2.253 × 10⁹⁶(97-digit number)

22537570730429358145…43509823404990842879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.253 × 10⁹⁶(97-digit number)

22537570730429358145…43509823404990842881

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

4.507 × 10⁹⁶(97-digit number)

45075141460858716291…87019646809981685759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.507 × 10⁹⁶(97-digit number)

45075141460858716291…87019646809981685761

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

9.015 × 10⁹⁶(97-digit number)

90150282921717432583…74039293619963371519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.015 × 10⁹⁶(97-digit number)

90150282921717432583…74039293619963371521

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 #3,505,267

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