Block #21,614

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 2:59:24 PM · Difficulty 7.9453 · 6,795,218 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

387f2c42bcfaf3d88ab1055fdcdbee33881901d4fbbe8fafd141df0fd8902a3d

View on Chainz ↗

Height

#21,614

Difficulty

7.945303

Transactions

Size

505 B

Version

Bits

07f1ff68

Nonce

669

Timestamp

7/12/2013, 2:59:24 PM

Confirmations

6,795,218

Mined by

⛏️ P2SHAVLTojg127vdfmkE2T8rPwTuSfKaFN1Rch

Merkle Root

8d9d946c6ffdca6cd2291cbadf486e3f854c767418fd42d2339dd5b781dfc885

Transactions (2)

Coinbase5d0f38c92f85e6…c19ef60a6d0138

1 in → 1 out15.8300 XPM108 B

AVLTojg1…KaFN1Rch

e781ffdf806d14…ccd08e0ca58f83

2 in → 1 out15.9700 XPM308 B

AXPRySWh…GeFZKjLU

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.

3.159 × 10⁹³(94-digit number)

31599268834901276361…02089432856773874439

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

3.159 × 10⁹³(94-digit number)

31599268834901276361…02089432856773874439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.159 × 10⁹³(94-digit number)

31599268834901276361…02089432856773874441

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

6.319 × 10⁹³(94-digit number)

63198537669802552722…04178865713547748879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.319 × 10⁹³(94-digit number)

63198537669802552722…04178865713547748881

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

1.263 × 10⁹⁴(95-digit number)

12639707533960510544…08357731427095497759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.263 × 10⁹⁴(95-digit number)

12639707533960510544…08357731427095497761

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

2.527 × 10⁹⁴(95-digit number)

25279415067921021088…16715462854190995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.527 × 10⁹⁴(95-digit number)

25279415067921021088…16715462854190995521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #21,614

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