Block #1,554,395

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2016, 4:46:33 PM · Difficulty 10.6604 · 5,290,952 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e801066729467dfa3fd8ba4a14415c1b613e6f557246f0d24f6348a9f056194

View on Chainz ↗

Height

#1,554,395

Difficulty

10.660427

Transactions

Size

869 B

Version

Bits

0aa911b7

Nonce

183,420,562

Timestamp

4/23/2016, 4:46:33 PM

Confirmations

5,290,952

Mined by

⛏️ P2SHAPeoVDtcz8g7PTXY4ReKSiUnSuqzLbrpsT

Merkle Root

bc8077f5645ef8cc078e453a55f003705dc1fa5983e61cf94918c00ed1f23503

Transactions (2)

Coinbasef3acdd0bc61621…5f90a3fa9a6472

1 in → 1 out8.8000 XPM109 B

APeoVDtc…qzLbrpsT

d98935c14232ff…1f7c70cd7bd4d0

4 in → 2 out8.9351 XPM670 B

AaNk9yMv…GNMAzBcU AWahMYTs…ctLPyz1b

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.

2.126 × 10⁹⁴(95-digit number)

21261040939398912616…57237987296144061929

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

2.126 × 10⁹⁴(95-digit number)

21261040939398912616…57237987296144061929

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.126 × 10⁹⁴(95-digit number)

21261040939398912616…57237987296144061931

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

4.252 × 10⁹⁴(95-digit number)

42522081878797825232…14475974592288123859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.252 × 10⁹⁴(95-digit number)

42522081878797825232…14475974592288123861

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

8.504 × 10⁹⁴(95-digit number)

85044163757595650464…28951949184576247719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.504 × 10⁹⁴(95-digit number)

85044163757595650464…28951949184576247721

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

1.700 × 10⁹⁵(96-digit number)

17008832751519130092…57903898369152495439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.700 × 10⁹⁵(96-digit number)

17008832751519130092…57903898369152495441

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

3.401 × 10⁹⁵(96-digit number)

34017665503038260185…15807796738304990879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.401 × 10⁹⁵(96-digit number)

34017665503038260185…15807796738304990881

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 #1,554,395

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