Block #274,995

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 12:33:02 PM · Difficulty 9.9594 · 6,520,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08dd59450f4a1220545481a24941d666ae41f9a63dca3f92cad0fa69a6b13937

View on Chainz ↗

Height

#274,995

Difficulty

9.959435

Transactions

Size

877 B

Version

Bits

09f59d8b

Nonce

181,079

Timestamp

11/26/2013, 12:33:02 PM

Confirmations

6,520,908

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f1415d33c9976cd369a693841d1d8086aef518ffd9734a143e4815fc31d7e3e9

Transactions (4)

Coinbased3814ed38db10e…f1038c512323f2

1 in → 1 out10.1000 XPM110 B

AeKNrjNj…1NEq95Ta

07ade3f6c1487a…2598761ff561fd

1 in → 2 out10.0700 XPM226 B

Ad6bt69S…PfMPqrnD AdzNo4s5…Dd7sYzxa

013741ca237dab…737041c6f3505b

1 in → 2 out9.0587 XPM226 B

ALTTMZ6H…pCSfmTCK APDFiiZT…oqxnymU8

c67709abf015e3…377439c875c8c0

1 in → 2 out4.9454 XPM226 B

AUhzdfjC…W2uom5Q8 AWBkqPMM…QnvK8aGb

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.

2.512 × 10⁹²(93-digit number)

25126417690084922696…93008830936824063519

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

2.512 × 10⁹²(93-digit number)

25126417690084922696…93008830936824063519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.512 × 10⁹²(93-digit number)

25126417690084922696…93008830936824063521

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

5.025 × 10⁹²(93-digit number)

50252835380169845392…86017661873648127039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.025 × 10⁹²(93-digit number)

50252835380169845392…86017661873648127041

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

1.005 × 10⁹³(94-digit number)

10050567076033969078…72035323747296254079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.005 × 10⁹³(94-digit number)

10050567076033969078…72035323747296254081

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

2.010 × 10⁹³(94-digit number)

20101134152067938157…44070647494592508159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.010 × 10⁹³(94-digit number)

20101134152067938157…44070647494592508161

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

4.020 × 10⁹³(94-digit number)

40202268304135876314…88141294989185016319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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