Block #270,133

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 5:41:41 PM · Difficulty 9.9518 · 6,524,916 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

10a9b222f625616b045f659a81399e0ee087547008f9029bb71d680c76fe383d

View on Chainz ↗

Height

#270,133

Difficulty

9.951820

Transactions

Size

1.65 KB

Version

Bits

09f3aa78

Nonce

30,571

Timestamp

11/23/2013, 5:41:41 PM

Confirmations

6,524,916

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

69d99985ce2411d78927bdf2448647131026f91320d5993a6b848a8786117c3e

Transactions (5)

Coinbase3d8c6490210b27…42a394c8bf092d

1 in → 1 out10.1300 XPM109 B

AeKNrjNj…1NEq95Ta

03c3224445c1c4…2aa1480ab47738

3 in → 2 out9.1768 XPM522 B

ASoMqgFL…Mqqt2fHC AKtwSk6i…vifEVgVe

09b22366e8d241…7c803a0dbfda16

1 in → 2 out0.8200 XPM226 B

AWKhcKD1…AK1RJ4a3 AMxzwjrE…EC6Cs6WK

33ee1437c1cbf3…6a5fe7f35a3488

1 in → 2 out1.9700 XPM225 B

ARTMLLVV…VDXUyGNS AHQqDe2x…cccBnpcF

d79a203d84a025…864c8466d0581d

3 in → 2 out1.0113 XPM520 B

AKtKx1wF…QUarQRPR ASzbY4Nj…U6RYutUU

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.

5.426 × 10⁸⁷(88-digit number)

54261189922090506380…30032611590651395999

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

5.426 × 10⁸⁷(88-digit number)

54261189922090506380…30032611590651395999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.426 × 10⁸⁷(88-digit number)

54261189922090506380…30032611590651396001

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

1.085 × 10⁸⁸(89-digit number)

10852237984418101276…60065223181302791999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.085 × 10⁸⁸(89-digit number)

10852237984418101276…60065223181302792001

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

2.170 × 10⁸⁸(89-digit number)

21704475968836202552…20130446362605583999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.170 × 10⁸⁸(89-digit number)

21704475968836202552…20130446362605584001

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

4.340 × 10⁸⁸(89-digit number)

43408951937672405104…40260892725211167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.340 × 10⁸⁸(89-digit number)

43408951937672405104…40260892725211168001

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

8.681 × 10⁸⁸(89-digit number)

86817903875344810208…80521785450422335999

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