Block #3,503,922

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2020, 1:23:35 PM · Difficulty 10.9309 · 3,333,009 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4c2e9858ea2b531cbf552352cdaee53404c39402f3c1a6c37dc628c81989660

View on Chainz ↗

Height

#3,503,922

Difficulty

10.930865

Transactions

Size

22.00 KB

Version

Bits

0aee4d27

Nonce

605,678,211

Timestamp

1/7/2020, 1:23:35 PM

Confirmations

3,333,009

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

ca0817e55ce4b6fe2ac00f77d1cac80a96953def0cd3c47336bada9ddfb4f5c2

Transactions (4)

Coinbase29b717fec8b522…72ffe958f5776e

1 in → 1 out8.6000 XPM110 B

ASiq2qtK…VMhmk7yL

ed8b123db33470…afe9b6605dbe8a

50 in → 1 out249.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

b7469acc2fe3c1…4b65558bb2748c

50 in → 1 out249.9171 XPM7.26 KB

ALcTQaSP…1C5Yf2Zi

f3310d16b22d58…090dd80ec087ac

50 in → 1 out4904.8110 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.

1.070 × 10⁹⁶(97-digit number)

10706942812634620810…66260210490354461439

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

1.070 × 10⁹⁶(97-digit number)

10706942812634620810…66260210490354461439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.070 × 10⁹⁶(97-digit number)

10706942812634620810…66260210490354461441

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

2.141 × 10⁹⁶(97-digit number)

21413885625269241620…32520420980708922879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.141 × 10⁹⁶(97-digit number)

21413885625269241620…32520420980708922881

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

4.282 × 10⁹⁶(97-digit number)

42827771250538483240…65040841961417845759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.282 × 10⁹⁶(97-digit number)

42827771250538483240…65040841961417845761

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

8.565 × 10⁹⁶(97-digit number)

85655542501076966480…30081683922835691519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.565 × 10⁹⁶(97-digit number)

85655542501076966480…30081683922835691521

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

1.713 × 10⁹⁷(98-digit number)

17131108500215393296…60163367845671383039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.713 × 10⁹⁷(98-digit number)

17131108500215393296…60163367845671383041

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 #3,503,922

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