Block #641,226

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/20/2014, 8:05:53 PM · Difficulty 10.9574 · 6,168,475 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

380743459016db396d44903b7cce668aa27a92e4494c7de8c72d74ebd74a812a

View on Chainz ↗

Height

#641,226

Difficulty

10.957426

Transactions

Size

501 B

Version

Bits

0af519e6

Nonce

3,075,274,100

Timestamp

7/20/2014, 8:05:53 PM

Confirmations

6,168,475

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

83ed60746c12c9301bce0d417b16ad2244d464dba1532d0c42cc6b57048634a2

Transactions (2)

Coinbase8397d07aab03d1…959fcb75dca8d0

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

ba95fe27e73ace…968ec0f2a84795

1 in → 4 out6.2887 XPM294 B

AXDEZh15…FbrAPGkC AeKNrjNj…1NEq95Ta AXAbEwxW…93h2qQtb AKinBSz6…c5jHh6RZ

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.

4.026 × 10⁹⁶(97-digit number)

40266238867182967157…11184627500345575679

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

4.026 × 10⁹⁶(97-digit number)

40266238867182967157…11184627500345575679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.026 × 10⁹⁶(97-digit number)

40266238867182967157…11184627500345575681

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

8.053 × 10⁹⁶(97-digit number)

80532477734365934315…22369255000691151359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.053 × 10⁹⁶(97-digit number)

80532477734365934315…22369255000691151361

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

1.610 × 10⁹⁷(98-digit number)

16106495546873186863…44738510001382302719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.610 × 10⁹⁷(98-digit number)

16106495546873186863…44738510001382302721

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

3.221 × 10⁹⁷(98-digit number)

32212991093746373726…89477020002764605439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.221 × 10⁹⁷(98-digit number)

32212991093746373726…89477020002764605441

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

6.442 × 10⁹⁷(98-digit number)

64425982187492747452…78954040005529210879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.442 × 10⁹⁷(98-digit number)

64425982187492747452…78954040005529210881

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

1.288 × 10⁹⁸(99-digit number)

12885196437498549490…57908080011058421759

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 #641,226

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