Block #2,101,853

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/5/2017, 11:06:57 PM · Difficulty 10.8648 · 4,738,278 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89fa077b7d92190990bde574a08a525654352d138daedc28787ba219e003859d

View on Chainz ↗

Height

#2,101,853

Difficulty

10.864834

Transactions

Size

244 B

Version

Bits

0add65be

Nonce

1,340,619,228

Timestamp

5/5/2017, 11:06:57 PM

Confirmations

4,738,278

Mined by

⛏️ P2SHAXdAFibKnCTZAMoZ6FFPE5s1XtNchjjM1Y

Merkle Root

6118e91fee1d98841637365dfe3a3fe840968b9ed66b19e676c7551e071a7b4f

Transactions (1)

Coinbase6118e91fee1d98…c7551e071a7b4f

1 in → 2 out8.4600 XPM152 B

AXdAFibK…NchjjM1Y AXbk7f7A…Tx7JECPG

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.

4.046 × 10⁹⁹(100-digit number)

40461160344464561195…00777211154076794879

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

4.046 × 10⁹⁹(100-digit number)

40461160344464561195…00777211154076794879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.046 × 10⁹⁹(100-digit number)

40461160344464561195…00777211154076794881

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

8.092 × 10⁹⁹(100-digit number)

80922320688929122390…01554422308153589759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.092 × 10⁹⁹(100-digit number)

80922320688929122390…01554422308153589761

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

1.618 × 10¹⁰⁰(101-digit number)

16184464137785824478…03108844616307179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.618 × 10¹⁰⁰(101-digit number)

16184464137785824478…03108844616307179521

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

3.236 × 10¹⁰⁰(101-digit number)

32368928275571648956…06217689232614359039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.236 × 10¹⁰⁰(101-digit number)

32368928275571648956…06217689232614359041

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

6.473 × 10¹⁰⁰(101-digit number)

64737856551143297912…12435378465228718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.473 × 10¹⁰⁰(101-digit number)

64737856551143297912…12435378465228718081

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 #2,101,853

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