Block #3,057,008

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/17/2019, 3:39:05 PM · Difficulty 11.0082 · 3,785,470 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b931db2da235663aee12aaae363aa747e716e1a97a4273b77adb285c5dd5fc79

View on Chainz ↗

Height

#3,057,008

Difficulty

11.008202

Transactions

Size

722 B

Version

Bits

0b02198c

Nonce

1,046,720

Timestamp

2/17/2019, 3:39:05 PM

Confirmations

3,785,470

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

ab2c906bc4474c428ed06c95025e395527af27687bc6d380c69100bf29056ede

Transactions (2)

Coinbaseecb7d47f0c34a3…97c6152ab9bb5f

1 in → 1 out8.2500 XPM110 B

AUMQRepm…tAfKmdW1

d16bd860b00596…cb5cfb15d58907

3 in → 2 out1091.2587 XPM522 B

AeTHTL7A…vT1872bk ASbentJC…qRaaqyk5

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.

4.914 × 10⁹³(94-digit number)

49146938212747571965…93018273572139967999

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

4.914 × 10⁹³(94-digit number)

49146938212747571965…93018273572139967999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.914 × 10⁹³(94-digit number)

49146938212747571965…93018273572139968001

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

9.829 × 10⁹³(94-digit number)

98293876425495143931…86036547144279935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.829 × 10⁹³(94-digit number)

98293876425495143931…86036547144279936001

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

1.965 × 10⁹⁴(95-digit number)

19658775285099028786…72073094288559871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.965 × 10⁹⁴(95-digit number)

19658775285099028786…72073094288559872001

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

3.931 × 10⁹⁴(95-digit number)

39317550570198057572…44146188577119743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.931 × 10⁹⁴(95-digit number)

39317550570198057572…44146188577119744001

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

7.863 × 10⁹⁴(95-digit number)

78635101140396115145…88292377154239487999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.863 × 10⁹⁴(95-digit number)

78635101140396115145…88292377154239488001

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

1.572 × 10⁹⁵(96-digit number)

15727020228079223029…76584754308478975999

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 #3,057,008

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