Block #1,437,483

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2016, 5:04:59 PM · Difficulty 10.7936 · 5,389,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dec821d8f5617e8854eff716d1fcb9c40ca612ce00ca95c57c5ace9d3c0b7f72

View on Chainz ↗

Height

#1,437,483

Difficulty

10.793569

Transactions

Size

2.44 KB

Version

Bits

0acb275c

Nonce

720,060,069

Timestamp

1/31/2016, 5:04:59 PM

Confirmations

5,389,673

Mined by

⛏️ P2SHAQiTjTB11y6cweKS4N36iti1ih7BU5pjZt

Merkle Root

b3ff16e941db1be43a3d4a28dd19af86ab64def59b73f314f6d7d4ce334d5171

Transactions (2)

Coinbase5300f3378c1696…6f805f3e60666b

1 in → 1 out8.6000 XPM109 B

AQiTjTB1…7BU5pjZt

6c9b4d6476457f…799f1316789e69

15 in → 2 out195.0406 XPM2.24 KB

ALDhofhm…9n9dwnxh AJVeRHXf…C2yREH1f

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.

2.005 × 10⁹⁸(99-digit number)

20058386340364445874…24930279989796044799

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

2.005 × 10⁹⁸(99-digit number)

20058386340364445874…24930279989796044799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.005 × 10⁹⁸(99-digit number)

20058386340364445874…24930279989796044801

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

4.011 × 10⁹⁸(99-digit number)

40116772680728891749…49860559979592089599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.011 × 10⁹⁸(99-digit number)

40116772680728891749…49860559979592089601

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

8.023 × 10⁹⁸(99-digit number)

80233545361457783499…99721119959184179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.023 × 10⁹⁸(99-digit number)

80233545361457783499…99721119959184179201

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

1.604 × 10⁹⁹(100-digit number)

16046709072291556699…99442239918368358399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.604 × 10⁹⁹(100-digit number)

16046709072291556699…99442239918368358401

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

3.209 × 10⁹⁹(100-digit number)

32093418144583113399…98884479836736716799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.209 × 10⁹⁹(100-digit number)

32093418144583113399…98884479836736716801

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 #1,437,483

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