Block #2,621,156

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/19/2018, 5:46:21 PM · Difficulty 11.2319 · 4,182,300 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acbec81f5c6ea7eb29b0dba583120a769f0b47c55f055698cac430e24a24235d

View on Chainz ↗

Height

#2,621,156

Difficulty

11.231861

Transactions

Size

95.66 KB

Version

Bits

0b3b5b43

Nonce

355,122,941

Timestamp

4/19/2018, 5:46:21 PM

Confirmations

4,182,300

Mined by

⛏️ P2SHAHh9zZFoZbBnutximAfxf6VfRAUugRvTuV

Merkle Root

1051d751cfa947c6d99637e604133e25ba69b1ccf0c60e210609a2e8fe7c5bd3

Transactions (2)

Coinbasea9dec19c297247…d6081285c577e5

1 in → 1 out8.8900 XPM109 B

AHh9zZFo…UugRvTuV

a4389f653eb6dc…6264a7e417a142

660 in → 2 out160.0100 XPM95.46 KB

AJufJCVg…xFp2JcGm ALPF8J52…Hjw4BMsG

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.

2.629 × 10⁹⁶(97-digit number)

26298222328175717400…17154959955189570559

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

2.629 × 10⁹⁶(97-digit number)

26298222328175717400…17154959955189570559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.629 × 10⁹⁶(97-digit number)

26298222328175717400…17154959955189570561

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

5.259 × 10⁹⁶(97-digit number)

52596444656351434801…34309919910379141119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.259 × 10⁹⁶(97-digit number)

52596444656351434801…34309919910379141121

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

1.051 × 10⁹⁷(98-digit number)

10519288931270286960…68619839820758282239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.051 × 10⁹⁷(98-digit number)

10519288931270286960…68619839820758282241

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

2.103 × 10⁹⁷(98-digit number)

21038577862540573920…37239679641516564479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.103 × 10⁹⁷(98-digit number)

21038577862540573920…37239679641516564481

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

4.207 × 10⁹⁷(98-digit number)

42077155725081147841…74479359283033128959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.207 × 10⁹⁷(98-digit number)

42077155725081147841…74479359283033128961

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

8.415 × 10⁹⁷(98-digit number)

84154311450162295682…48958718566066257919

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