Block #2,260,436

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/20/2017, 5:27:18 PM · Difficulty 10.9519 · 4,573,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d37b7b8500cfbf212dcaa5824ded07e1a551e11a77efe5cc54043dcf11b09123

View on Chainz ↗

Height

#2,260,436

Difficulty

10.951859

Transactions

Size

425 B

Version

Bits

0af3ad09

Nonce

1,290,832,748

Timestamp

8/20/2017, 5:27:18 PM

Confirmations

4,573,272

Mined by

⛏️ P2SHAedxkHPzh4sGo6mKDWeHACbbnPi1dTwSZX

Merkle Root

47ab7c09e4152c51aa90e32c2cf9aa5683f7fea31f76191922972dbba2275f10

Transactions (2)

Coinbase37ee34a4fd5433…2247b482d1addd

1 in → 1 out8.3300 XPM110 B

AedxkHPz…i1dTwSZX

64df712c07bdf6…4c506517ef0d56

1 in → 2 out35687.9125 XPM225 B

AYRxTstj…BxPsoefe AJUviksm…TkigMSLb

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.

2.672 × 10⁹⁵(96-digit number)

26728671154906498575…57112273378012349119

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

2.672 × 10⁹⁵(96-digit number)

26728671154906498575…57112273378012349119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.672 × 10⁹⁵(96-digit number)

26728671154906498575…57112273378012349121

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

5.345 × 10⁹⁵(96-digit number)

53457342309812997151…14224546756024698239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.345 × 10⁹⁵(96-digit number)

53457342309812997151…14224546756024698241

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

1.069 × 10⁹⁶(97-digit number)

10691468461962599430…28449093512049396479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.069 × 10⁹⁶(97-digit number)

10691468461962599430…28449093512049396481

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

2.138 × 10⁹⁶(97-digit number)

21382936923925198860…56898187024098792959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.138 × 10⁹⁶(97-digit number)

21382936923925198860…56898187024098792961

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

4.276 × 10⁹⁶(97-digit number)

42765873847850397721…13796374048197585919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.276 × 10⁹⁶(97-digit number)

42765873847850397721…13796374048197585921

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

8.553 × 10⁹⁶(97-digit number)

85531747695700795443…27592748096395171839

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

Block #2,260,436

Cookie Preferences