Block #2,921,878

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/13/2018, 10:54:30 PM · Difficulty 11.3754 · 3,910,985 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3beb19aae70b390fa984789cb6e0b8a085e54d4b0d3e97a592b77f63f7bdc8cb

View on Chainz ↗

Height

#2,921,878

Difficulty

11.375393

Transactions

Size

427 B

Version

Bits

0b6019ba

Nonce

1,605,911,768

Timestamp

11/13/2018, 10:54:30 PM

Confirmations

3,910,985

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

c94ed0cba2fbcd567ca920ec2e6ff6d9bd6143977be55347af257239ee52fefd

Transactions (2)

Coinbaseb43089a389ab23…37395035bc6e42

1 in → 1 out7.7300 XPM110 B

AbXwmGxD…4XXYP765

e16fd44a114550…ecf0431c4c2759

1 in → 2 out4143.1209 XPM226 B

AcHiW94D…XBYgvBW6 AWrEGZFD…UB4ETKW7

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.

7.165 × 10⁹⁵(96-digit number)

71658621506092737521…31589622353032631439

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

7.165 × 10⁹⁵(96-digit number)

71658621506092737521…31589622353032631439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.165 × 10⁹⁵(96-digit number)

71658621506092737521…31589622353032631441

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

1.433 × 10⁹⁶(97-digit number)

14331724301218547504…63179244706065262879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.433 × 10⁹⁶(97-digit number)

14331724301218547504…63179244706065262881

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

2.866 × 10⁹⁶(97-digit number)

28663448602437095008…26358489412130525759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.866 × 10⁹⁶(97-digit number)

28663448602437095008…26358489412130525761

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

5.732 × 10⁹⁶(97-digit number)

57326897204874190017…52716978824261051519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.732 × 10⁹⁶(97-digit number)

57326897204874190017…52716978824261051521

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

1.146 × 10⁹⁷(98-digit number)

11465379440974838003…05433957648522103039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.146 × 10⁹⁷(98-digit number)

11465379440974838003…05433957648522103041

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

2.293 × 10⁹⁷(98-digit number)

22930758881949676007…10867915297044206079

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 #2,921,878

Cookie Preferences