Block #3,174,001

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2019, 9:48:09 PM · Difficulty 11.3053 · 3,665,730 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3328f08ceeb157ea9fdb45a74c02e8caeecada0b380a01706b35a3e9d3669dc7

View on Chainz ↗

Height

#3,174,001

Difficulty

11.305281

Transactions

Size

1.43 KB

Version

Bits

0b4e26e4

Nonce

333,142,728

Timestamp

5/8/2019, 9:48:09 PM

Confirmations

3,665,730

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

2fe4c473c05857a3ef890e5328f2ae743f22210de333feccd83d3f92406bbc28

Transactions (4)

Coinbaseb3e2f36fd72255…88404fea771548

1 in → 1 out7.8400 XPM110 B

AUMQRepm…tAfKmdW1

43eb716ba1181e…224e91597484bc

7 in → 2 out54.5900 XPM877 B

ARx5pvS5…qXT1H2zv AbXwmGxD…4XXYP765

3d7dd862963ec1…55d6a4c7ff9073

1 in → 2 out7.7900 XPM193 B

Aa5pBbPn…rSa6pBDT AbXwmGxD…4XXYP765

e2f2e6297df998…1e0456d46f848a

1 in → 2 out7.7900 XPM192 B

AUGtTmZd…kasJyqf5 AbXwmGxD…4XXYP765

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.

2.351 × 10⁹⁴(95-digit number)

23516978829475742590…71444936623271634999

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

2.351 × 10⁹⁴(95-digit number)

23516978829475742590…71444936623271634999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.351 × 10⁹⁴(95-digit number)

23516978829475742590…71444936623271635001

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

4.703 × 10⁹⁴(95-digit number)

47033957658951485180…42889873246543269999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.703 × 10⁹⁴(95-digit number)

47033957658951485180…42889873246543270001

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

9.406 × 10⁹⁴(95-digit number)

94067915317902970361…85779746493086539999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.406 × 10⁹⁴(95-digit number)

94067915317902970361…85779746493086540001

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

1.881 × 10⁹⁵(96-digit number)

18813583063580594072…71559492986173079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.881 × 10⁹⁵(96-digit number)

18813583063580594072…71559492986173080001

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

3.762 × 10⁹⁵(96-digit number)

37627166127161188144…43118985972346159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.762 × 10⁹⁵(96-digit number)

37627166127161188144…43118985972346160001

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

7.525 × 10⁹⁵(96-digit number)

75254332254322376288…86237971944692319999

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 #3,174,001

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