Block #642,033

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/21/2014, 10:22:13 AM · Difficulty 10.9570 · 6,185,123 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06b73d2c363ccaa66735fe76647345580d4727fad79d05bc6db2b9de279ace0c

View on Chainz ↗

Height

#642,033

Difficulty

10.957030

Transactions

Size

97.23 KB

Version

Bits

0af4fff1

Nonce

222,520,593

Timestamp

7/21/2014, 10:22:13 AM

Confirmations

6,185,123

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

02ce7f8a60fb353f401ef91f8cd4550e934adafa61da3c08db8a0c76150acfb0

Transactions (3)

Coinbase69a33bd81a9baa…8b56cdf559db3e

1 in → 1 out9.3200 XPM116 B

ANSXnLY2…Sd25TjkD

0d55b1de6f496e…2ba04d8a5e3e9b

334 in → 2 out1000.0100 XPM48.37 KB

AaUAHKKY…96UvUJn4 AJTmBTjZ…DnfQGwqJ

21aec979f62542…9927efad9c2e77

336 in → 2 out1000.0100 XPM48.66 KB

AaUAHKKY…96UvUJn4 AVnThpHn…wDCYLMJ8

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.

2.070 × 10⁹⁸(99-digit number)

20708864452714534114…72974125358187642879

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

2.070 × 10⁹⁸(99-digit number)

20708864452714534114…72974125358187642879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.070 × 10⁹⁸(99-digit number)

20708864452714534114…72974125358187642881

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

4.141 × 10⁹⁸(99-digit number)

41417728905429068228…45948250716375285759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.141 × 10⁹⁸(99-digit number)

41417728905429068228…45948250716375285761

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

8.283 × 10⁹⁸(99-digit number)

82835457810858136457…91896501432750571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.283 × 10⁹⁸(99-digit number)

82835457810858136457…91896501432750571521

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

1.656 × 10⁹⁹(100-digit number)

16567091562171627291…83793002865501143039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.656 × 10⁹⁹(100-digit number)

16567091562171627291…83793002865501143041

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

3.313 × 10⁹⁹(100-digit number)

33134183124343254582…67586005731002286079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.313 × 10⁹⁹(100-digit number)

33134183124343254582…67586005731002286081

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

6.626 × 10⁹⁹(100-digit number)

66268366248686509165…35172011462004572159

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 #642,033

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