Block #948,251

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2015, 1:25:59 AM · Difficulty 10.8995 · 5,848,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c2dc84bbc7ec80fd2aa184475d6e341151e64b6944a9a7c53fca50fe9ab5e1c

View on Chainz ↗

Height

#948,251

Difficulty

10.899512

Transactions

Size

2.05 KB

Version

Bits

0ae64664

Nonce

789,945,698

Timestamp

2/23/2015, 1:25:59 AM

Confirmations

5,848,198

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c812b72a177d1dfea5b12c979e03cccd3f893d41c7f8fce3f9c42af652aa9c64

Transactions (2)

Coinbase031e0aca8c4da6…f7c658888915ff

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

ae2cf81015c070…9fcc4568659ea3

1 in → 51 out7.9527 XPM1.85 KB

AcAYXubV…72sadqng AJbrnBZF…MPSNLyYD AYXjbYcw…ejkoCK3K ALY1bK9U…yQSPXGJN AH5g9Bje…B9a1b8tN

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.

4.644 × 10⁹⁶(97-digit number)

46444017509521171769…34926867890784545919

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

4.644 × 10⁹⁶(97-digit number)

46444017509521171769…34926867890784545919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.644 × 10⁹⁶(97-digit number)

46444017509521171769…34926867890784545921

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

9.288 × 10⁹⁶(97-digit number)

92888035019042343538…69853735781569091839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.288 × 10⁹⁶(97-digit number)

92888035019042343538…69853735781569091841

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

1.857 × 10⁹⁷(98-digit number)

18577607003808468707…39707471563138183679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.857 × 10⁹⁷(98-digit number)

18577607003808468707…39707471563138183681

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

3.715 × 10⁹⁷(98-digit number)

37155214007616937415…79414943126276367359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.715 × 10⁹⁷(98-digit number)

37155214007616937415…79414943126276367361

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

7.431 × 10⁹⁷(98-digit number)

74310428015233874830…58829886252552734719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.431 × 10⁹⁷(98-digit number)

74310428015233874830…58829886252552734721

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