Block #1,427,602

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2016, 1:06:10 PM · Difficulty 10.7476 · 5,388,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4d809d158061bc054d3c19ae319989cf9fae75c701d589b420d488ed60205d08

View on Chainz ↗

Height

#1,427,602

Difficulty

10.747614

Transactions

Size

971 B

Version

Bits

0abf63a7

Nonce

130,816,714

Timestamp

1/25/2016, 1:06:10 PM

Confirmations

5,388,707

Mined by

⛏️ P2SHAZjRPCnomjbynfrvRk77kN7xQDhwAss6Hf

Merkle Root

4aff76740e7eb3642b5352724e9faafc2036d08a8ffcc354bbb3452124cf2d74

Transactions (2)

Coinbase3f681b322009c2…732fb89cabf888

1 in → 1 out8.6500 XPM110 B

AZjRPCno…hwAss6Hf

53bf914feb3ec0…3922938e0ba596

1 in → 18 out221.2325 XPM770 B

ATTa8X84…rM4yhgRc Ae2kAYdw…7cYg8ff6 AKPXjByo…VKXWyt83 AGASukeT…P66DBeKo AbqFvYDk…raK1JUK8

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.

2.402 × 10⁹⁶(97-digit number)

24028515069797281209…68044917750816261119

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

2.402 × 10⁹⁶(97-digit number)

24028515069797281209…68044917750816261119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.402 × 10⁹⁶(97-digit number)

24028515069797281209…68044917750816261121

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

4.805 × 10⁹⁶(97-digit number)

48057030139594562419…36089835501632522239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.805 × 10⁹⁶(97-digit number)

48057030139594562419…36089835501632522241

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

9.611 × 10⁹⁶(97-digit number)

96114060279189124839…72179671003265044479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.611 × 10⁹⁶(97-digit number)

96114060279189124839…72179671003265044481

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

1.922 × 10⁹⁷(98-digit number)

19222812055837824967…44359342006530088959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.922 × 10⁹⁷(98-digit number)

19222812055837824967…44359342006530088961

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

3.844 × 10⁹⁷(98-digit number)

38445624111675649935…88718684013060177919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.844 × 10⁹⁷(98-digit number)

38445624111675649935…88718684013060177921

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 #1,427,602

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