Block #47,831

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 12:38:02 PM · Difficulty 8.8305 · 6,777,692 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bd1c232436b22e33792bf9f39af640caaa10a3c38346f3023dfec5d4892aa21

View on Chainz ↗

Height

#47,831

Difficulty

8.830494

Transactions

Size

1.05 KB

Version

Bits

08d49b49

Nonce

732

Timestamp

7/15/2013, 12:38:02 PM

Confirmations

6,777,692

Mined by

⛏️ P2SHAeMmEUPwR3YBXrxF2XGMmPyyahJPthik2i

Merkle Root

8127f5dbabc621530cf207e445269ac6478573ffafcd46463b17f6c96f0d52c5

Transactions (3)

Coinbasecd3455b7681b19…9390d88d9f7b17

1 in → 1 out12.8300 XPM110 B

AeMmEUPw…JPthik2i

f1977d42f9390f…a13c1ebea57ef9

2 in → 2 out26.7800 XPM305 B

AbjLQB3Y…SXLCXwVY APE4qb5N…spoLCkiv

f7c889eae25714…9dd3d148319e40

4 in → 2 out40.4500 XPM566 B

ALi1myfS…QCVHkjbq AToR53XS…LJekc8eY

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.

9.020 × 10⁹⁵(96-digit number)

90200308724084139710…09020561541345896669

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

9.020 × 10⁹⁵(96-digit number)

90200308724084139710…09020561541345896669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.020 × 10⁹⁵(96-digit number)

90200308724084139710…09020561541345896671

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

1.804 × 10⁹⁶(97-digit number)

18040061744816827942…18041123082691793339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.804 × 10⁹⁶(97-digit number)

18040061744816827942…18041123082691793341

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

3.608 × 10⁹⁶(97-digit number)

36080123489633655884…36082246165383586679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.608 × 10⁹⁶(97-digit number)

36080123489633655884…36082246165383586681

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

7.216 × 10⁹⁶(97-digit number)

72160246979267311768…72164492330767173359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.216 × 10⁹⁶(97-digit number)

72160246979267311768…72164492330767173361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #47,831

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