Block #1,385,850

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2015, 11:06:45 AM · Difficulty 10.8138 · 5,418,952 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c402590a694a83e18bfedfca5210fe59a2a64fad104dbfecba03176f4d2787f

View on Chainz ↗

Height

#1,385,850

Difficulty

10.813794

Transactions

Size

1.11 KB

Version

Bits

0ad054d5

Nonce

8,708,712

Timestamp

12/26/2015, 11:06:45 AM

Confirmations

5,418,952

Mined by

⛏️ P2SHAJxXLvWjVxPRoMFzMFd1Me88ua55gw2z4Q

Merkle Root

f5d052215137a900852aceb3638e11415d504cb61dd8e90fc746f874997c2535

Transactions (2)

Coinbase46bb293bac5836…ad09045252d045

1 in → 1 out8.5500 XPM109 B

AJxXLvWj…55gw2z4Q

878e1c59b0e8a5…49b31ec810b371

1 in → 23 out141.0409 XPM939 B

AMJBuh7q…srTWv9ZJ Acu2vSA4…9S7kiP64 ATUW1u6X…YYAQqaKM AKXMbKS4…tFFYXQPi Ac2mpfHM…RYztA5d8

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.

1.376 × 10⁹⁷(98-digit number)

13761813671878405102…27416450423754874879

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

1.376 × 10⁹⁷(98-digit number)

13761813671878405102…27416450423754874879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.376 × 10⁹⁷(98-digit number)

13761813671878405102…27416450423754874881

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

2.752 × 10⁹⁷(98-digit number)

27523627343756810205…54832900847509749759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.752 × 10⁹⁷(98-digit number)

27523627343756810205…54832900847509749761

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

5.504 × 10⁹⁷(98-digit number)

55047254687513620411…09665801695019499519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.504 × 10⁹⁷(98-digit number)

55047254687513620411…09665801695019499521

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

1.100 × 10⁹⁸(99-digit number)

11009450937502724082…19331603390038999039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.100 × 10⁹⁸(99-digit number)

11009450937502724082…19331603390038999041

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

2.201 × 10⁹⁸(99-digit number)

22018901875005448164…38663206780077998079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.201 × 10⁹⁸(99-digit number)

22018901875005448164…38663206780077998081

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