Block #3,505,516

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2020, 4:44:56 PM · Difficulty 10.9303 · 3,327,454 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

38a09df5b99cfb2ddee49582c65360ce1fcffdd4e02a3c16a511ecba52d806fd

View on Chainz ↗

Height

#3,505,516

Difficulty

10.930265

Transactions

Size

14.72 KB

Version

Bits

0aee25d5

Nonce

136,928,265

Timestamp

1/8/2020, 4:44:56 PM

Confirmations

3,327,454

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

9603b07f30ee68e58c2d65529678379328730b81b8d90aaf212affba3b5615ac

Transactions (3)

Coinbase60a46140594059…4d4f35401249ae

1 in → 1 out8.5200 XPM109 B

ASiq2qtK…VMhmk7yL

94a5d810b0d207…c82c5ae841544f

50 in → 1 out199.9200 XPM7.26 KB

ALcTQaSP…1C5Yf2Zi

6a971ea85ccf1d…54f02b4e5cb6d9

50 in → 1 out199.9200 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.

3.005 × 10⁹³(94-digit number)

30059632281689849993…54931354980896975359

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

3.005 × 10⁹³(94-digit number)

30059632281689849993…54931354980896975359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.005 × 10⁹³(94-digit number)

30059632281689849993…54931354980896975361

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

6.011 × 10⁹³(94-digit number)

60119264563379699986…09862709961793950719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.011 × 10⁹³(94-digit number)

60119264563379699986…09862709961793950721

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

1.202 × 10⁹⁴(95-digit number)

12023852912675939997…19725419923587901439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.202 × 10⁹⁴(95-digit number)

12023852912675939997…19725419923587901441

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

2.404 × 10⁹⁴(95-digit number)

24047705825351879994…39450839847175802879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.404 × 10⁹⁴(95-digit number)

24047705825351879994…39450839847175802881

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

4.809 × 10⁹⁴(95-digit number)

48095411650703759989…78901679694351605759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.809 × 10⁹⁴(95-digit number)

48095411650703759989…78901679694351605761

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 #3,505,516

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