Block #360,618

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 1:35:36 PM · Difficulty 10.3959 · 6,449,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

271c5bff8d5d67058bf1cf8d2ca5bee6d977582d3bccf2165f7325cbd16f264c

View on Chainz ↗

Height

#360,618

Difficulty

10.395895

Transactions

Size

1.23 KB

Version

Bits

0a655968

Nonce

107,138

Timestamp

1/15/2014, 1:35:36 PM

Confirmations

6,449,074

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

24d813f3a8c317073318b35259e67f18c0cc6630e135d6a815d89d3fde126e6a

Transactions (2)

Coinbased6fad9fc3728a0…95a41f9df72e42

1 in → 26 out9.2400 XPM947 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AJLB8H7s…MRD4s5wA

fbbce7d423ac7e…cfdb51fd941bcd

1 in → 2 out6.1754 XPM226 B

ANF7g3eT…f1hFcx6D AWhqCNs1…mTz9bU71

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.

3.497 × 10⁹⁶(97-digit number)

34974307748658118671…04615468367376202179

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

3.497 × 10⁹⁶(97-digit number)

34974307748658118671…04615468367376202179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.497 × 10⁹⁶(97-digit number)

34974307748658118671…04615468367376202181

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

6.994 × 10⁹⁶(97-digit number)

69948615497316237342…09230936734752404359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.994 × 10⁹⁶(97-digit number)

69948615497316237342…09230936734752404361

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

1.398 × 10⁹⁷(98-digit number)

13989723099463247468…18461873469504808719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.398 × 10⁹⁷(98-digit number)

13989723099463247468…18461873469504808721

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

2.797 × 10⁹⁷(98-digit number)

27979446198926494937…36923746939009617439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.797 × 10⁹⁷(98-digit number)

27979446198926494937…36923746939009617441

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

5.595 × 10⁹⁷(98-digit number)

55958892397852989874…73847493878019234879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.595 × 10⁹⁷(98-digit number)

55958892397852989874…73847493878019234881

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 #360,618

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