Block #1,246,673

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/21/2015, 5:04:22 PM · Difficulty 10.7521 · 5,570,165 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a221cc8f0ad6dbced25c44576897f450102ab8948a1c5b40d5b8b4edfb22214

View on Chainz ↗

Height

#1,246,673

Difficulty

10.752140

Transactions

Size

2.44 KB

Version

Bits

0ac08c46

Nonce

1,933,127,685

Timestamp

9/21/2015, 5:04:22 PM

Confirmations

5,570,165

Mined by

⛏️ P2SHAK2JdrLy6mCwBioNgyfiYqv8aiAfCBz3r3

Merkle Root

ab018a37de793363c2c619a9f44b4cf6c4fa93a405bcb7acc45c808a4580d2cf

Transactions (4)

Coinbase7bb298420ece53…581fc41e4e1f7a

1 in → 1 out8.6800 XPM109 B

AK2JdrLy…AfCBz3r3

9d3cd73c6a66d1…9a587e5e2725a3

6 in → 2 out50.7765 XPM966 B

AXZf8xqq…hQwCQgXt ALjorDNN…mKAc9KJW

96b9373595d796…809b78df16da3a

1 in → 28 out163.1688 XPM1.08 KB

AaFkfDnf…6J84Mo1n ASnjKGbo…do6DRkmm AeFjQ6Ta…dc5cZ5Lg AMuNAQx1…1F2pRV2X ANT6FYei…mwuM7Nif

6fbafdce3f1744…529b01cfb18e96

1 in → 2 out3.3224 XPM226 B

AcuM7XiJ…5uND8Jce AX4rX6ad…GfPLBog4

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.

2.227 × 10⁹⁶(97-digit number)

22273307891322896056…74352841330375577599

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

2.227 × 10⁹⁶(97-digit number)

22273307891322896056…74352841330375577599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.227 × 10⁹⁶(97-digit number)

22273307891322896056…74352841330375577601

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

4.454 × 10⁹⁶(97-digit number)

44546615782645792113…48705682660751155199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.454 × 10⁹⁶(97-digit number)

44546615782645792113…48705682660751155201

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

8.909 × 10⁹⁶(97-digit number)

89093231565291584227…97411365321502310399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.909 × 10⁹⁶(97-digit number)

89093231565291584227…97411365321502310401

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

1.781 × 10⁹⁷(98-digit number)

17818646313058316845…94822730643004620799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.781 × 10⁹⁷(98-digit number)

17818646313058316845…94822730643004620801

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

3.563 × 10⁹⁷(98-digit number)

35637292626116633690…89645461286009241599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.563 × 10⁹⁷(98-digit number)

35637292626116633690…89645461286009241601

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 #1,246,673

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