Block #2,149,930

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/7/2017, 9:46:00 AM · Difficulty 10.8983 · 4,689,740 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc73d02b5519c2ff75e940cdf2941297a8b08a3585f8ee6adb478b6c14f90658

View on Chainz ↗

Height

#2,149,930

Difficulty

10.898284

Transactions

Size

654 B

Version

Bits

0ae5f5f2

Nonce

948,735,233

Timestamp

6/7/2017, 9:46:00 AM

Confirmations

4,689,740

Mined by

⛏️ P2SHAULRtHHk8qhVEKsyQtMxh9nusCJLYwPa3s

Merkle Root

0b168fe49bd52e140e6ddccbc79ab57ec808dee0734a92bf7e3f84d4692cf210

Transactions (3)

Coinbase7a1ee150359151…8758f658e93b74

1 in → 1 out8.4300 XPM110 B

AULRtHHk…JLYwPa3s

720b21af956f8a…43f05da5e506cf

1 in → 2 out75296.1808 XPM227 B

AXGoiojv…ra52FvPE AWSpM1vT…ukZRfqjD

3053280854f7cc…7100a12108bb7e

1 in → 2 out74623.6044 XPM226 B

AWSpM1vT…ukZRfqjD AaZhMNJK…ULbJpKEp

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.

4.712 × 10⁹⁷(98-digit number)

47120422016000363791…76245136920920432639

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

4.712 × 10⁹⁷(98-digit number)

47120422016000363791…76245136920920432639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.712 × 10⁹⁷(98-digit number)

47120422016000363791…76245136920920432641

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

9.424 × 10⁹⁷(98-digit number)

94240844032000727583…52490273841840865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.424 × 10⁹⁷(98-digit number)

94240844032000727583…52490273841840865281

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

1.884 × 10⁹⁸(99-digit number)

18848168806400145516…04980547683681730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.884 × 10⁹⁸(99-digit number)

18848168806400145516…04980547683681730561

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

3.769 × 10⁹⁸(99-digit number)

37696337612800291033…09961095367363461119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.769 × 10⁹⁸(99-digit number)

37696337612800291033…09961095367363461121

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

7.539 × 10⁹⁸(99-digit number)

75392675225600582066…19922190734726922239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.539 × 10⁹⁸(99-digit number)

75392675225600582066…19922190734726922241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,149,930

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