Block #267,339

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/21/2013, 5:11:55 AM · Difficulty 9.9591 · 6,522,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72db8d1dcdb120c081bd684d46615933b7d41a5bdb48645893c3c035d7293c6e

View on Chainz ↗

Height

#267,339

Difficulty

9.959070

Transactions

Size

1.75 KB

Version

Bits

09f58595

Nonce

287,699

Timestamp

11/21/2013, 5:11:55 AM

Confirmations

6,522,532

Merkle Root

b6808c382e63ad4c1c2708dbf1a4c5d33f2db1d3c1f9d8758d2b92733a863011

Transactions (4)

Coinbasef151754e03bc15…7fad343f0ee884

1 in → 1 out10.1000 XPM100 B

AbGkvdxH…oihMdBXd

53b358c2015c15…d3501f3e805a65

3 in → 2 out50.0104 XPM520 B

AGkLo1di…APZPGe8B AV1L8npR…44QHGSYf

b25b45aba59def…506d378498fe71

1 in → 4 out10.0500 XPM260 B

Ae4nk4M8…o2o9BXBP AZSVhd9Y…rYTSwNV1 AMuPGPXT…eMMNvd8v AeKNrjNj…1NEq95Ta

a111f3b34e074c…4b70d64b39cbc8

5 in → 2 out19.9100 XPM819 B

AXUme5BG…nGVsr2WZ AbJvBqrs…Cdc3gKro

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.

3.395 × 10⁹⁴(95-digit number)

33953607882032859169…01417907851017135359

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

3.395 × 10⁹⁴(95-digit number)

33953607882032859169…01417907851017135359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.395 × 10⁹⁴(95-digit number)

33953607882032859169…01417907851017135361

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

6.790 × 10⁹⁴(95-digit number)

67907215764065718339…02835815702034270719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.790 × 10⁹⁴(95-digit number)

67907215764065718339…02835815702034270721

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

1.358 × 10⁹⁵(96-digit number)

13581443152813143667…05671631404068541439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.358 × 10⁹⁵(96-digit number)

13581443152813143667…05671631404068541441

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

2.716 × 10⁹⁵(96-digit number)

27162886305626287335…11343262808137082879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.716 × 10⁹⁵(96-digit number)

27162886305626287335…11343262808137082881

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

5.432 × 10⁹⁵(96-digit number)

54325772611252574671…22686525616274165759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.432 × 10⁹⁵(96-digit number)

54325772611252574671…22686525616274165761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.086 × 10⁹⁶(97-digit number)

10865154522250514934…45373051232548331519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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