Block #2,939,749

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/26/2018, 9:13:50 AM · Difficulty 11.3728 · 3,898,970 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e07518184f1db5f4852d379ed9cf6a186dcdf760985a128b0098c72d0c6602b2

View on Chainz ↗

Height

#2,939,749

Difficulty

11.372809

Transactions

Size

1.61 KB

Version

Bits

0b5f706f

Nonce

715,054,348

Timestamp

11/26/2018, 9:13:50 AM

Confirmations

3,898,970

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

ced5991b813bb6e0506e99cefa68679df1ce860ad2b7418f709c666c5ca76365

Transactions (2)

Coinbasefc0e7e856afe74…88b01bf3718736

1 in → 1 out7.7400 XPM110 B

AUhjokok…k5m93PZR

ce7390b504fc1d…dc8183154b17fd

9 in → 3 out2532.2077 XPM1.41 KB

AeoYRFM9…akPhgXp7 AaCt2Z2e…QB2Doko7 AeU6Hdjc…cvWHdukb

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.

7.973 × 10⁹⁶(97-digit number)

79739340822249050243…56442235382260523519

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

7.973 × 10⁹⁶(97-digit number)

79739340822249050243…56442235382260523519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.973 × 10⁹⁶(97-digit number)

79739340822249050243…56442235382260523521

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

1.594 × 10⁹⁷(98-digit number)

15947868164449810048…12884470764521047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.594 × 10⁹⁷(98-digit number)

15947868164449810048…12884470764521047041

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

3.189 × 10⁹⁷(98-digit number)

31895736328899620097…25768941529042094079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.189 × 10⁹⁷(98-digit number)

31895736328899620097…25768941529042094081

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

6.379 × 10⁹⁷(98-digit number)

63791472657799240194…51537883058084188159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.379 × 10⁹⁷(98-digit number)

63791472657799240194…51537883058084188161

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

1.275 × 10⁹⁸(99-digit number)

12758294531559848038…03075766116168376319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.275 × 10⁹⁸(99-digit number)

12758294531559848038…03075766116168376321

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

2.551 × 10⁹⁸(99-digit number)

25516589063119696077…06151532232336752639

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 #2,939,749

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