Block #268,880

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 12:54:27 PM · Difficulty 9.9561 · 6,522,949 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

097dceea25f94dd38f7a4eb9fd0bd3b5f02c84f004bd5b295d0fda376de2f741

View on Chainz ↗

Height

#268,880

Difficulty

9.956078

Transactions

Size

11.26 KB

Version

Bits

09f4c18f

Nonce

34,862

Timestamp

11/22/2013, 12:54:27 PM

Confirmations

6,522,949

Merkle Root

6749a3d3733c118d94a3134a980ceacaef6c17cbe39d99f1f088d71e66d768b8

Transactions (4)

Coinbasef9bec69ce08cf0…f008b738bda648

1 in → 1 out10.2000 XPM109 B

APfdpKWo…9D88GFDR

16c3ecbf21502f…e75df41efd8ed5

2 in → 2 out236.7415 XPM375 B

AWYToJ1s…PP84dTQc AaY4Jxm9…bktBfnBq

31b788b31bcc0f…6900e9788b6045

6 in → 2 out10.0100 XPM964 B

AQymV7KA…mRb8ZEtT AMfPS3GG…MhHVB1fu

5c01eb3c73a22e…35f895aded4081

67 in → 2 out34.7715 XPM9.76 KB

AY3qHuiM…QgXBRHfu AGSVxxXb…oMoruhWF

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.

4.208 × 10⁹⁴(95-digit number)

42081018058040650072…77707560326753273999

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

4.208 × 10⁹⁴(95-digit number)

42081018058040650072…77707560326753273999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.208 × 10⁹⁴(95-digit number)

42081018058040650072…77707560326753274001

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

8.416 × 10⁹⁴(95-digit number)

84162036116081300145…55415120653506547999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.416 × 10⁹⁴(95-digit number)

84162036116081300145…55415120653506548001

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

1.683 × 10⁹⁵(96-digit number)

16832407223216260029…10830241307013095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.683 × 10⁹⁵(96-digit number)

16832407223216260029…10830241307013096001

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

3.366 × 10⁹⁵(96-digit number)

33664814446432520058…21660482614026191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.366 × 10⁹⁵(96-digit number)

33664814446432520058…21660482614026192001

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

6.732 × 10⁹⁵(96-digit number)

67329628892865040116…43320965228052383999

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