Block #1,634,008

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2016, 1:56:09 PM · Difficulty 10.6010 · 5,192,662 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ec7e981f71b172da8cdb2c074a65bb47e43d3b68f8413e1911cd40c1d19bb3a

View on Chainz ↗

Height

#1,634,008

Difficulty

10.601019

Transactions

Size

5.04 KB

Version

Bits

0a99dc5c

Nonce

141,252,589

Timestamp

6/18/2016, 1:56:09 PM

Confirmations

5,192,662

Mined by

⛏️ P2SHAQhqXaj4CvNm8GrLCkaENnQZmaguENZSbi

Merkle Root

c9cb3f729261e30349f14a5f0a08945b5ce8c55edba832b827bf15c1a2430645

Transactions (2)

Coinbase85e99bc1b3b241…b3ac434e6369f3

1 in → 1 out8.9300 XPM109 B

AQhqXaj4…guENZSbi

e34f84b4e5fd30…1222a636e5fb12

33 in → 2 out2689.8160 XPM4.85 KB

AQCgayPh…MYK75NPP APMpyMBo…WmDC4HGV

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.

4.553 × 10⁹⁶(97-digit number)

45530985548537697948…42413128171900723199

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

4.553 × 10⁹⁶(97-digit number)

45530985548537697948…42413128171900723199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.553 × 10⁹⁶(97-digit number)

45530985548537697948…42413128171900723201

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

9.106 × 10⁹⁶(97-digit number)

91061971097075395897…84826256343801446399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.106 × 10⁹⁶(97-digit number)

91061971097075395897…84826256343801446401

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

1.821 × 10⁹⁷(98-digit number)

18212394219415079179…69652512687602892799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.821 × 10⁹⁷(98-digit number)

18212394219415079179…69652512687602892801

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

3.642 × 10⁹⁷(98-digit number)

36424788438830158359…39305025375205785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.642 × 10⁹⁷(98-digit number)

36424788438830158359…39305025375205785601

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

7.284 × 10⁹⁷(98-digit number)

72849576877660316718…78610050750411571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.284 × 10⁹⁷(98-digit number)

72849576877660316718…78610050750411571201

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 #1,634,008

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