Block #2,513,348

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/9/2018, 11:08:20 PM · Difficulty 10.9789 · 4,320,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3370653d34e90305c32e10509b99c445fda783ae1bfe99c2c018f8e4e112e75b

View on Chainz ↗

Height

#2,513,348

Difficulty

10.978852

Transactions

Size

576 B

Version

Bits

0afa9608

Nonce

299,987,856

Timestamp

2/9/2018, 11:08:20 PM

Confirmations

4,320,574

Mined by

⛏️ P2SHAU4fkKniDqfgVZ8sCLTpbzr6D49PDbH1oM

Merkle Root

d3c8d0988c32d3aa390a2cfdf0162473661b03e11e46d3b93168f43b7eacbd58

Transactions (2)

Coinbaseb9d1a10d7e676f…abbda8cbec43a2

1 in → 1 out8.2900 XPM110 B

AU4fkKni…9PDbH1oM

e16d3e3b0a7429…3b7afec20a9701

2 in → 2 out33.0802 XPM375 B

AW7AvowP…ZLUY2HhH AcpKwKfN…6qjP7EVR

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.

1.660 × 10⁹⁶(97-digit number)

16603465653233788668…58887552520324382719

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

1.660 × 10⁹⁶(97-digit number)

16603465653233788668…58887552520324382719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.660 × 10⁹⁶(97-digit number)

16603465653233788668…58887552520324382721

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

3.320 × 10⁹⁶(97-digit number)

33206931306467577337…17775105040648765439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.320 × 10⁹⁶(97-digit number)

33206931306467577337…17775105040648765441

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

6.641 × 10⁹⁶(97-digit number)

66413862612935154675…35550210081297530879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.641 × 10⁹⁶(97-digit number)

66413862612935154675…35550210081297530881

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

1.328 × 10⁹⁷(98-digit number)

13282772522587030935…71100420162595061759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.328 × 10⁹⁷(98-digit number)

13282772522587030935…71100420162595061761

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

2.656 × 10⁹⁷(98-digit number)

26565545045174061870…42200840325190123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.656 × 10⁹⁷(98-digit number)

26565545045174061870…42200840325190123521

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

5.313 × 10⁹⁷(98-digit number)

53131090090348123740…84401680650380247039

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 #2,513,348

Cookie Preferences