Block #196,023

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 5:28:53 AM · Difficulty 9.8802 · 6,613,790 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9fae2a23b794377c40e5b27d241b62db1846d753310976398891c8a995199128

View on Chainz ↗

Height

#196,023

Difficulty

9.880202

Transactions

Size

3.47 KB

Version

Bits

09e154e7

Nonce

1,164,823,679

Timestamp

10/6/2013, 5:28:53 AM

Confirmations

6,613,790

Mined by

⛏️ RPANAVEjQmEH3np5pV6gNDL2E2S36wqP126u

Merkle Root

7672db1bfaa44226d0621429fda1303d91bf54cdb31c4e6451450fd8da987239

Transactions (1)

Coinbase7672db1bfaa442…450fd8da987239

1 in → 100 out10.1900 XPM3.38 KB

ANAVEjQm…6wqP126u Ae54SB9E…Aow3zWsK AebfwVBz…ZtQwaXb8 AR7hUyNW…iuooRCti AUeg7gsi…EW5EsuUL

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.

4.842 × 10⁹⁷(98-digit number)

48420915208920933639…76694318917718507519

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

4.842 × 10⁹⁷(98-digit number)

48420915208920933639…76694318917718507519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.842 × 10⁹⁷(98-digit number)

48420915208920933639…76694318917718507521

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

9.684 × 10⁹⁷(98-digit number)

96841830417841867279…53388637835437015039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.684 × 10⁹⁷(98-digit number)

96841830417841867279…53388637835437015041

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

1.936 × 10⁹⁸(99-digit number)

19368366083568373455…06777275670874030079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.936 × 10⁹⁸(99-digit number)

19368366083568373455…06777275670874030081

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

3.873 × 10⁹⁸(99-digit number)

38736732167136746911…13554551341748060159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.873 × 10⁹⁸(99-digit number)

38736732167136746911…13554551341748060161

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

7.747 × 10⁹⁸(99-digit number)

77473464334273493823…27109102683496120319

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 #196,023

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