Block #1,950,204

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/22/2017, 11:50:21 PM · Difficulty 10.7270 · 4,891,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8ad71d50fbb58e7fc836dcc8069cf61739b15a9b2cae75a0a32954fcb8b62d1

View on Chainz ↗

Height

#1,950,204

Difficulty

10.727045

Transactions

Size

1.14 KB

Version

Bits

0aba1fa1

Nonce

1,623,939,776

Timestamp

1/22/2017, 11:50:21 PM

Confirmations

4,891,758

Mined by

⛏️ P2SHAHiQi4oecVSoKn7cjqxDeU4gquqVVqZRgT

Merkle Root

26ee0f5ecec41426f4f184e560ab6fa6518380e4b1c68c2e5a9f6b445ee86347

Transactions (2)

Coinbase8358a7e135c51e…97e8711f347ade

1 in → 1 out8.6900 XPM109 B

AHiQi4oe…qVVqZRgT

6f0a0dcfa3d1a1…54cea8c64f0890

6 in → 2 out669.3685 XPM966 B

AZ7xo3ni…aXTAFhZR AZ45tbge…3pSD9wRx

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.

2.339 × 10⁹⁶(97-digit number)

23390112898346873565…36113822577512509439

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

2.339 × 10⁹⁶(97-digit number)

23390112898346873565…36113822577512509439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.339 × 10⁹⁶(97-digit number)

23390112898346873565…36113822577512509441

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

4.678 × 10⁹⁶(97-digit number)

46780225796693747130…72227645155025018879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.678 × 10⁹⁶(97-digit number)

46780225796693747130…72227645155025018881

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

9.356 × 10⁹⁶(97-digit number)

93560451593387494260…44455290310050037759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.356 × 10⁹⁶(97-digit number)

93560451593387494260…44455290310050037761

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

1.871 × 10⁹⁷(98-digit number)

18712090318677498852…88910580620100075519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.871 × 10⁹⁷(98-digit number)

18712090318677498852…88910580620100075521

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

3.742 × 10⁹⁷(98-digit number)

37424180637354997704…77821161240200151039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.742 × 10⁹⁷(98-digit number)

37424180637354997704…77821161240200151041

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

7.484 × 10⁹⁷(98-digit number)

74848361274709995408…55642322480400302079

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 #1,950,204

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