Block #446,637

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 5:15:33 PM · Difficulty 10.3596 · 6,358,148 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cfc1514611b02b5341c7a88ed428290107aa7e16ba7435e563c440f4c1e8c22

View on Chainz ↗

Height

#446,637

Difficulty

10.359630

Transactions

Size

16.70 KB

Version

Bits

0a5c10af

Nonce

24,500

Timestamp

3/16/2014, 5:15:33 PM

Confirmations

6,358,148

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

299dde3409e2adf3680d0407d8b8f1793dd5c62fa7444ed686b32fe291f79f86

Transactions (4)

Coinbasef3ee7b387ecb01…3b17b61d02a29e

1 in → 1 out9.4903 XPM116 B

AbwWkWZt…kawDhufa

f28d9e1bea2c14…181f380d38ffdb

109 in → 2 out383.6057 XPM15.83 KB

AcBvLaSu…X3gaHvJ1 AZ77qyWv…XkbNNZZd

2fb26f7f6b96fc…09bc43e762c08d

2 in → 1 out6.0959 XPM341 B

AdFNdRL8…Bwo6SeRo

aa4d550bfa055a…1f55656da307fb

2 in → 1 out3.0080 XPM340 B

AGKj1VZw…bhwpBHGN

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.

1.127 × 10⁹⁷(98-digit number)

11274389452955009644…77446003993943013359

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

1.127 × 10⁹⁷(98-digit number)

11274389452955009644…77446003993943013359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.127 × 10⁹⁷(98-digit number)

11274389452955009644…77446003993943013361

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

2.254 × 10⁹⁷(98-digit number)

22548778905910019289…54892007987886026719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.254 × 10⁹⁷(98-digit number)

22548778905910019289…54892007987886026721

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

4.509 × 10⁹⁷(98-digit number)

45097557811820038579…09784015975772053439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.509 × 10⁹⁷(98-digit number)

45097557811820038579…09784015975772053441

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

9.019 × 10⁹⁷(98-digit number)

90195115623640077159…19568031951544106879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.019 × 10⁹⁷(98-digit number)

90195115623640077159…19568031951544106881

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

1.803 × 10⁹⁸(99-digit number)

18039023124728015431…39136063903088213759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.803 × 10⁹⁸(99-digit number)

18039023124728015431…39136063903088213761

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