Block #893,050

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/13/2015, 1:36:54 AM · Difficulty 10.9517 · 5,903,553 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f0bb8a945f0a79b3dddc448baabfdf2c7348a4ec8f58a997f9dcaa26cd16ad4

View on Chainz ↗

Height

#893,050

Difficulty

10.951679

Transactions

Size

660 B

Version

Bits

0af3a13e

Nonce

178,932,357

Timestamp

1/13/2015, 1:36:54 AM

Confirmations

5,903,553

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f173147c36065463f3000f27661e897176b4056fe38e22afbabfc500b23fc4da

Transactions (3)

Coinbase9b2a040a756012…a923d5577d37e9

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

694ea157fe4dc6…53fc0b9b050e10

1 in → 2 out8.3000 XPM226 B

AcAXPjdF…vkvmCNdL AMuYYsgd…ioD1TEUt

303141b6241621…41d65d5efae01f

1 in → 2 out8.3000 XPM226 B

AN15uUyU…uqoxW2Bk AGEed55R…9o5EJWws

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.

9.400 × 10⁹⁸(99-digit number)

94002667832684093995…41468959502012415999

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

9.400 × 10⁹⁸(99-digit number)

94002667832684093995…41468959502012415999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.400 × 10⁹⁸(99-digit number)

94002667832684093995…41468959502012416001

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

1.880 × 10⁹⁹(100-digit number)

18800533566536818799…82937919004024831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.880 × 10⁹⁹(100-digit number)

18800533566536818799…82937919004024832001

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

3.760 × 10⁹⁹(100-digit number)

37601067133073637598…65875838008049663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.760 × 10⁹⁹(100-digit number)

37601067133073637598…65875838008049664001

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

7.520 × 10⁹⁹(100-digit number)

75202134266147275196…31751676016099327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.520 × 10⁹⁹(100-digit number)

75202134266147275196…31751676016099328001

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

1.504 × 10¹⁰⁰(101-digit number)

15040426853229455039…63503352032198655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.504 × 10¹⁰⁰(101-digit number)

15040426853229455039…63503352032198656001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.008 × 10¹⁰⁰(101-digit number)

30080853706458910078…27006704064397311999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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