Block #2,461,177

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2018, 4:09:07 AM · Difficulty 10.9552 · 4,380,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3bffea62575de2f5399a273ec8b48b5091ddb605fe0382b10d14e14528a581ba

View on Chainz ↗

Height

#2,461,177

Difficulty

10.955188

Transactions

Size

1.00 KB

Version

Bits

0af4872d

Nonce

149,913,703

Timestamp

1/7/2018, 4:09:07 AM

Confirmations

4,380,920

Mined by

⛏️ P2SHAGXMt9BPSp88UC9jmJyhNNA7xzyiqUe4J2

Merkle Root

f38a1945dbd673275235ef49a98b2e51fe674aeb44d31c39ab6e5ace42f64505

Transactions (4)

Coinbase37f097441789f4…0b412c2a594edd

1 in → 1 out8.3500 XPM109 B

AGXMt9BP…yiqUe4J2

2f37be1c5ab815…d2bbdf0b6777c7

1 in → 2 out5939.9900 XPM226 B

AXwsmPPr…6VMrFrtM AWXkQBH7…Wcr931qS

5d6c6bcd1df0cd…dfee542ce1fe47

1 in → 2 out6012.4660 XPM226 B

AGKsVJox…2a7pCemF AU7xkW52…RMPvkSaU

b2079ed4e8959c…1cafa5d1bb10f0

2 in → 2 out601.3449 XPM376 B

ALjLjYzh…ehX7Jx55 Ade3LKUp…qr8mPBKF

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.

1.397 × 10⁹⁶(97-digit number)

13974174895073287870…62171264175284392959

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

1.397 × 10⁹⁶(97-digit number)

13974174895073287870…62171264175284392959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.397 × 10⁹⁶(97-digit number)

13974174895073287870…62171264175284392961

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

2.794 × 10⁹⁶(97-digit number)

27948349790146575740…24342528350568785919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.794 × 10⁹⁶(97-digit number)

27948349790146575740…24342528350568785921

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

5.589 × 10⁹⁶(97-digit number)

55896699580293151481…48685056701137571839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.589 × 10⁹⁶(97-digit number)

55896699580293151481…48685056701137571841

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

1.117 × 10⁹⁷(98-digit number)

11179339916058630296…97370113402275143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.117 × 10⁹⁷(98-digit number)

11179339916058630296…97370113402275143681

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

2.235 × 10⁹⁷(98-digit number)

22358679832117260592…94740226804550287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.235 × 10⁹⁷(98-digit number)

22358679832117260592…94740226804550287361

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 #2,461,177

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