Block #279,093

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 5:45:31 AM · Difficulty 9.9707 · 6,533,650 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a690200cf6fc59d3805b8b979b07f6a4dfe4f1218075a62ed99ffb6918b8c28a

View on Chainz ↗

Height

#279,093

Difficulty

9.970731

Transactions

Size

1.04 KB

Version

Bits

09f881d0

Nonce

6,002

Timestamp

11/28/2013, 5:45:31 AM

Confirmations

6,533,650

Mined by

⛏️ 5BaRAbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

a470ecd4976a76d426a57dcd9d0b95be53832c98e8b13be00f77eec3c3d260bd

Transactions (1)

Coinbasea470ecd4976a76…77eec3c3d260bd

1 in → 27 out10.0400 XPM981 B

AbtgNzNb…9Atvu81w AM1xJMKk…x98BY7Nn AWtpYVWf…j9rRpU9c AJzWx2VD…j4ZSMit5 AQyr8Lw3…hs4nt3Pn

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.

1.097 × 10⁹³(94-digit number)

10974456608600839505…64118138585696255679

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

1.097 × 10⁹³(94-digit number)

10974456608600839505…64118138585696255679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.097 × 10⁹³(94-digit number)

10974456608600839505…64118138585696255681

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

2.194 × 10⁹³(94-digit number)

21948913217201679011…28236277171392511359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.194 × 10⁹³(94-digit number)

21948913217201679011…28236277171392511361

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

4.389 × 10⁹³(94-digit number)

43897826434403358022…56472554342785022719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.389 × 10⁹³(94-digit number)

43897826434403358022…56472554342785022721

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

8.779 × 10⁹³(94-digit number)

87795652868806716045…12945108685570045439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.779 × 10⁹³(94-digit number)

87795652868806716045…12945108685570045441

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

1.755 × 10⁹⁴(95-digit number)

17559130573761343209…25890217371140090879

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

Block #279,093

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