Block #3,503,832

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2020, 12:00:52 PM · Difficulty 10.9308 · 3,320,878 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56dc5e27dca7ff7b19c19ef6a5d6fe525a58b9d689fc6be24dd780fc3f081289

View on Chainz ↗

Height

#3,503,832

Difficulty

10.930772

Transactions

Size

21.99 KB

Version

Bits

0aee4719

Nonce

592,824,098

Timestamp

1/7/2020, 12:00:52 PM

Confirmations

3,320,878

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

6797e287c00ebbcefbc6ed61216193916c2b8a1e9b79c8d5e8f480dffc699d7d

Transactions (4)

Coinbase7b3284f4e027ba…e8075d1c97d2b7

1 in → 1 out8.6000 XPM110 B

ASiq2qtK…VMhmk7yL

4098e8447c9504…a64b881f3583aa

50 in → 1 out260.4969 XPM7.26 KB

ALcTQaSP…1C5Yf2Zi

01e3319007145f…bec9090ae09c04

50 in → 1 out260.3128 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

b5c51a05ee870a…ed154298214e33

50 in → 1 out2927.8790 XPM7.26 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.

2.649 × 10⁹⁴(95-digit number)

26497851690812431527…50212494097487871999

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

2.649 × 10⁹⁴(95-digit number)

26497851690812431527…50212494097487871999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.649 × 10⁹⁴(95-digit number)

26497851690812431527…50212494097487872001

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

5.299 × 10⁹⁴(95-digit number)

52995703381624863054…00424988194975743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.299 × 10⁹⁴(95-digit number)

52995703381624863054…00424988194975744001

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

1.059 × 10⁹⁵(96-digit number)

10599140676324972610…00849976389951487999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.059 × 10⁹⁵(96-digit number)

10599140676324972610…00849976389951488001

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

2.119 × 10⁹⁵(96-digit number)

21198281352649945221…01699952779902975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.119 × 10⁹⁵(96-digit number)

21198281352649945221…01699952779902976001

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

4.239 × 10⁹⁵(96-digit number)

42396562705299890443…03399905559805951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.239 × 10⁹⁵(96-digit number)

42396562705299890443…03399905559805952001

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 #3,503,832

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