Block #614,537

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/3/2014, 2:19:05 PM · Difficulty 10.9371 · 6,200,390 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

633cded835b047af18118e21bc885ab6beae3945f17003ed1563fe55ca371e35

View on Chainz ↗

Height

#614,537

Difficulty

10.937119

Transactions

Size

38.32 KB

Version

Bits

0aefe706

Nonce

117,647,798

Timestamp

7/3/2014, 2:19:05 PM

Confirmations

6,200,390

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ecf90b6158cc89016db25d7fc97421e2ac1066dda157c4fa0197ca03aae047bd

Transactions (4)

Coinbase43343082fe39f3…246e3e8f71fe77

1 in → 1 out8.7600 XPM116 B

ANSXnLY2…Sd25TjkD

8029e9e390eacc…2849b9e99ac5f2

258 in → 2 out79.3649 XPM37.38 KB

AZ3FbV3c…VPpAGUxZ AUnSuXXd…7nvcbgfG

8a87d97a158ca4…49299ba7b1f710

1 in → 2 out2.6643 XPM225 B

AJTsLJ89…rErdMt2e ANoqXDkz…MDZLdX55

28a46943069581…ad67528d552ca3

3 in → 2 out25.1400 XPM522 B

AaUNi76B…wtcm5mLM AcMjK72R…BjCNh4b8

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.

1.858 × 10⁹⁸(99-digit number)

18588144529996679379…75845008507714928639

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

1.858 × 10⁹⁸(99-digit number)

18588144529996679379…75845008507714928639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.858 × 10⁹⁸(99-digit number)

18588144529996679379…75845008507714928641

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

3.717 × 10⁹⁸(99-digit number)

37176289059993358759…51690017015429857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.717 × 10⁹⁸(99-digit number)

37176289059993358759…51690017015429857281

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

7.435 × 10⁹⁸(99-digit number)

74352578119986717518…03380034030859714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.435 × 10⁹⁸(99-digit number)

74352578119986717518…03380034030859714561

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

1.487 × 10⁹⁹(100-digit number)

14870515623997343503…06760068061719429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.487 × 10⁹⁹(100-digit number)

14870515623997343503…06760068061719429121

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

2.974 × 10⁹⁹(100-digit number)

29741031247994687007…13520136123438858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.974 × 10⁹⁹(100-digit number)

29741031247994687007…13520136123438858241

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 #614,537

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