Block #397,985

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 10:43:00 AM · Difficulty 10.4201 · 6,406,072 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78dd2bafcdec8559cb642b15f5ce52b163ce4705201000240285d59cac3265fa

View on Chainz ↗

Height

#397,985

Difficulty

10.420089

Transactions

Size

901 B

Version

Bits

0a6b8af7

Nonce

9,914

Timestamp

2/10/2014, 10:43:00 AM

Confirmations

6,406,072

Mined by

⛏️ aRdAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b125b3d33ae141d6d3dd808e817c3a7199e3b7c557819f3d6979bde2fe2b1375

Transactions (1)

Coinbaseb125b3d33ae141…79bde2fe2b1375

1 in → 22 out9.2000 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

9.762 × 10⁹³(94-digit number)

97628785801008408319…35698622463087823919

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

9.762 × 10⁹³(94-digit number)

97628785801008408319…35698622463087823919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.762 × 10⁹³(94-digit number)

97628785801008408319…35698622463087823921

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

1.952 × 10⁹⁴(95-digit number)

19525757160201681663…71397244926175647839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.952 × 10⁹⁴(95-digit number)

19525757160201681663…71397244926175647841

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

3.905 × 10⁹⁴(95-digit number)

39051514320403363327…42794489852351295679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.905 × 10⁹⁴(95-digit number)

39051514320403363327…42794489852351295681

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

7.810 × 10⁹⁴(95-digit number)

78103028640806726655…85588979704702591359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.810 × 10⁹⁴(95-digit number)

78103028640806726655…85588979704702591361

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

1.562 × 10⁹⁵(96-digit number)

15620605728161345331…71177959409405182719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.562 × 10⁹⁵(96-digit number)

15620605728161345331…71177959409405182721

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