Block #240,855

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/2/2013, 8:50:18 PM · Difficulty 9.9573 · 6,577,086 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2694c0dc58d5e02466a90a03467ef40a1eaebb0ad06eb04e0031a5fd70b66710

View on Chainz ↗

Height

#240,855

Difficulty

9.957262

Transactions

Size

1.43 KB

Version

Bits

09f50f1b

Nonce

4,985

Timestamp

11/2/2013, 8:50:18 PM

Confirmations

6,577,086

Mined by

⛏️ P2SHAaGLHY3qgdS3cPg37m3RkTiXFnCNghhoiL

Merkle Root

0ccb4f88cdcd36f85b06a15cbd113c0bed5ed566a7bf46810b6eb1b6e19b20ec

Transactions (4)

Coinbase2812e67187069e…6738ca506e5a8c

1 in → 1 out10.1000 XPM109 B

AaGLHY3q…CNghhoiL

eace6b3d5d7f96…4c78653a457afb

5 in → 2 out32.8440 XPM818 B

AVrW4vNy…QfkQ47o6 AGKoNE1X…7q441Win

9aece5413b867e…35af15c3efcc0a

1 in → 2 out10.0800 XPM225 B

ALB3Tqin…hrnNHQ3a Ae6Kku1N…Pp5i3uFY

3e7eafee1954c4…d2fe023c75e6f1

1 in → 2 out6.0592 XPM226 B

Abx5qH6G…Hh56BvNt AKpU79fr…uF9Dyujw

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.

1.352 × 10⁹⁷(98-digit number)

13522109322447359468…24704096784157890559

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

1.352 × 10⁹⁷(98-digit number)

13522109322447359468…24704096784157890559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.352 × 10⁹⁷(98-digit number)

13522109322447359468…24704096784157890561

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

2.704 × 10⁹⁷(98-digit number)

27044218644894718936…49408193568315781119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.704 × 10⁹⁷(98-digit number)

27044218644894718936…49408193568315781121

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

5.408 × 10⁹⁷(98-digit number)

54088437289789437873…98816387136631562239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.408 × 10⁹⁷(98-digit number)

54088437289789437873…98816387136631562241

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

1.081 × 10⁹⁸(99-digit number)

10817687457957887574…97632774273263124479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.081 × 10⁹⁸(99-digit number)

10817687457957887574…97632774273263124481

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

2.163 × 10⁹⁸(99-digit number)

21635374915915775149…95265548546526248959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.163 × 10⁹⁸(99-digit number)

21635374915915775149…95265548546526248961

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

Block #240,855

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