Block #261,291

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/15/2013, 12:42:57 PM · Difficulty 9.9731 · 6,529,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc18d0b8e16ef9218d2000f9c04caf4b95a2f93ace3abb72ff36413fe62a5689

View on Chainz ↗

Height

#261,291

Difficulty

9.973103

Transactions

Size

4.98 KB

Version

Bits

09f91d49

Nonce

250,248

Timestamp

11/15/2013, 12:42:57 PM

Confirmations

6,529,652

Merkle Root

05f396e3f48b18b1a4ad4e353015ac3365804df29ec1d85c0ea2cfe565e7c6c4

Transactions (5)

Coinbase04749777d8ceec…705c58972bdbbf

1 in → 1 out10.1200 XPM109 B

APSPDEoe…DMy5sRMt

ef9e568eb34af8…94516c6f0fba18

3 in → 2 out129.4207 XPM524 B

AMWzCVgo…AWwnBSsa AGXquKy4…xiRjhgQK

ba501a8c40a9a0…f2cdeeb734a5d5

26 in → 2 out59.0100 XPM3.83 KB

ANqNwUfL…YR8u7wDQ AGMc6AxZ…uXAB9yQp

ce5a4567cfac47…11c049d34df2ba

1 in → 2 out49.5861 XPM227 B

AKqrieY5…JxyNTZZZ AaWpv9an…nGjQzohz

a3fa64e92e71e9…72a7105aaa8c8b

1 in → 2 out143.2170 XPM225 B

AKrnAmdD…VJAPZpST AZdmkNt9…Dk8ffFeU

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.

1.088 × 10⁸⁹(90-digit number)

10884807351246432346…75601105890693786559

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

1.088 × 10⁸⁹(90-digit number)

10884807351246432346…75601105890693786559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.088 × 10⁸⁹(90-digit number)

10884807351246432346…75601105890693786561

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

2.176 × 10⁸⁹(90-digit number)

21769614702492864693…51202211781387573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.176 × 10⁸⁹(90-digit number)

21769614702492864693…51202211781387573121

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

4.353 × 10⁸⁹(90-digit number)

43539229404985729387…02404423562775146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.353 × 10⁸⁹(90-digit number)

43539229404985729387…02404423562775146241

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

8.707 × 10⁸⁹(90-digit number)

87078458809971458774…04808847125550292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.707 × 10⁸⁹(90-digit number)

87078458809971458774…04808847125550292481

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

1.741 × 10⁹⁰(91-digit number)

17415691761994291754…09617694251100584959

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