Block #1,507,627

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/22/2016, 12:57:19 PM · Difficulty 10.6255 · 5,309,586 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0bcac7329c7f6fde31b99c278bb402a121d0d73dbd6c3ac9dba776a30cdde525

View on Chainz ↗

Height

#1,507,627

Difficulty

10.625466

Transactions

Size

2.04 KB

Version

Bits

0aa01e91

Nonce

10,095,284

Timestamp

3/22/2016, 12:57:19 PM

Confirmations

5,309,586

Mined by

⛏️ P2SHAYkW8LHgpsktN7bPAfrpXhDhTREauEovY9

Merkle Root

59b5b5da9414854872127d3fed613bcae8440380dad7e591f0919084f5d3d10c

Transactions (2)

Coinbase4ddff71a627e49…511b73539c5e57

1 in → 1 out8.8600 XPM109 B

AYkW8LHg…EauEovY9

c4249826ddd65f…8b430b5b2450bb

1 in → 51 out128.7785 XPM1.85 KB

AdcFFzNr…XW2Q2UXo AXk1nfFx…qiuW4c8m ANiZfwQ2…CpK7Gc9u AaUeU9wm…LQ1Zzocu AcRJofch…a6zgLLJp

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.

8.513 × 10⁹⁷(98-digit number)

85131568855190534770…51308513107507609599

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

8.513 × 10⁹⁷(98-digit number)

85131568855190534770…51308513107507609599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.513 × 10⁹⁷(98-digit number)

85131568855190534770…51308513107507609601

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

1.702 × 10⁹⁸(99-digit number)

17026313771038106954…02617026215015219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.702 × 10⁹⁸(99-digit number)

17026313771038106954…02617026215015219201

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

3.405 × 10⁹⁸(99-digit number)

34052627542076213908…05234052430030438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.405 × 10⁹⁸(99-digit number)

34052627542076213908…05234052430030438401

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

6.810 × 10⁹⁸(99-digit number)

68105255084152427816…10468104860060876799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.810 × 10⁹⁸(99-digit number)

68105255084152427816…10468104860060876801

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

1.362 × 10⁹⁹(100-digit number)

13621051016830485563…20936209720121753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.362 × 10⁹⁹(100-digit number)

13621051016830485563…20936209720121753601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.724 × 10⁹⁹(100-digit number)

27242102033660971126…41872419440243507199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,507,627

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