Block #2,633,627

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 1:00:31 PM · Difficulty 11.2001 · 4,203,242 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b4a27c48f6bbcfb039c0636e73caec0e86977bbfa6ef3db61f4d1d2aeb36201

View on Chainz ↗

Height

#2,633,627

Difficulty

11.200148

Transactions

Size

1.86 KB

Version

Bits

0b333cee

Nonce

571,227,213

Timestamp

4/28/2018, 1:00:31 PM

Confirmations

4,203,242

Mined by

⛏️ P2SHAPzbRK8j4KB79WPAdaN2xamxeXLsqa3Ewv

Merkle Root

d5a79893888aec8f4bfff96d4f6ed475e1096d1eebb790602154d0b27a8fbd34

Transactions (5)

Coinbasea7c029d8e7d198…f31eabd60bb8f4

1 in → 1 out8.0100 XPM110 B

APzbRK8j…Lsqa3Ewv

894baa283a10ce…cd3abba80986ef

3 in → 17 out5595.1264 XPM1.01 KB

ARznVePF…S7wvbB9s ASk9H3sY…qUG8r1d4 AS4khYnr…fh8mQeBq AJgMrEpx…feT4viBK Adtn9f92…XZdrk6Uf

4c4b6f9eeac099…db774c3419727c

1 in → 2 out19350.8295 XPM226 B

AVx4kC3b…2SDnu89E AGTLpH6N…FPPjD5jk

1809943cfcd876…7f76d8f7599ef6

1 in → 2 out18356.8145 XPM225 B

AYfQtf58…xKLepLec AGTLpH6N…FPPjD5jk

1c8514dff6d544…77e9121ec216d7

1 in → 2 out17560.8045 XPM225 B

Ad5esw8E…XdqgCXuG AUfQ7V4g…djTs3Cis

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.

1.825 × 10⁹⁶(97-digit number)

18253747212944566631…91797468303417164799

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

1.825 × 10⁹⁶(97-digit number)

18253747212944566631…91797468303417164799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.825 × 10⁹⁶(97-digit number)

18253747212944566631…91797468303417164801

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

3.650 × 10⁹⁶(97-digit number)

36507494425889133262…83594936606834329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.650 × 10⁹⁶(97-digit number)

36507494425889133262…83594936606834329601

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

7.301 × 10⁹⁶(97-digit number)

73014988851778266525…67189873213668659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.301 × 10⁹⁶(97-digit number)

73014988851778266525…67189873213668659201

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

1.460 × 10⁹⁷(98-digit number)

14602997770355653305…34379746427337318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.460 × 10⁹⁷(98-digit number)

14602997770355653305…34379746427337318401

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

2.920 × 10⁹⁷(98-digit number)

29205995540711306610…68759492854674636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.920 × 10⁹⁷(98-digit number)

29205995540711306610…68759492854674636801

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

5.841 × 10⁹⁷(98-digit number)

58411991081422613220…37518985709349273599

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 #2,633,627

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