Block #215,136

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 9:40:04 PM · Difficulty 9.9250 · 6,592,788 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1329f2fa6a42526a7eb40cee880b708536965fa8980cee078c803ed1525db81

View on Chainz ↗

Height

#215,136

Difficulty

9.925014

Transactions

Size

4.10 KB

Version

Bits

09eccdbc

Nonce

1,164,815,703

Timestamp

10/17/2013, 9:40:04 PM

Confirmations

6,592,788

Mined by

⛏️ `HR`YAHtpSazSTy7HhDJGqd6f6eza4iaG5tNrSw

Merkle Root

144cf0258059da66e80dca456ad62f93945fd3c4052b7fb963d849996453a8fd

Transactions (1)

Coinbase144cf0258059da…d849996453a8fd

1 in → 119 out10.0813 XPM4.01 KB

AHtpSazS…aG5tNrSw AJKYzp1g…SvZiepke ATqDht7F…xHD53DYv AMV2CWW7…yebsFBrS AddsiWZi…H6Q5LUPW

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.

3.757 × 10⁹⁶(97-digit number)

37570811567103752024…80820927034037441919

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

3.757 × 10⁹⁶(97-digit number)

37570811567103752024…80820927034037441919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.757 × 10⁹⁶(97-digit number)

37570811567103752024…80820927034037441921

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

7.514 × 10⁹⁶(97-digit number)

75141623134207504048…61641854068074883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.514 × 10⁹⁶(97-digit number)

75141623134207504048…61641854068074883841

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

1.502 × 10⁹⁷(98-digit number)

15028324626841500809…23283708136149767679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.502 × 10⁹⁷(98-digit number)

15028324626841500809…23283708136149767681

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

3.005 × 10⁹⁷(98-digit number)

30056649253683001619…46567416272299535359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.005 × 10⁹⁷(98-digit number)

30056649253683001619…46567416272299535361

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

6.011 × 10⁹⁷(98-digit number)

60113298507366003238…93134832544599070719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #215,136

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