Block #368,290

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 3:23:41 PM · Difficulty 10.4412 · 6,442,424 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3a4ba4ed7fd4605b4113003c0f24f4f6bfa2e0946547b01819910e609c7089e

View on Chainz ↗

Height

#368,290

Difficulty

10.441161

Transactions

Size

229 B

Version

Bits

0a70eff1

Nonce

46,353

Timestamp

1/20/2014, 3:23:41 PM

Confirmations

6,442,424

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

f9c02783c7cdf3e69dcd22db8696f0cd1e6a6817ed56a06e4110b54523aaa2a5

Transactions (1)

Coinbasef9c02783c7cdf3…10b54523aaa2a5

1 in → 2 out9.1600 XPM136 B

ARmAMwyu…P7Kn74ZT AHsw4d6U…EnM8UXNZ

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.

2.305 × 10¹⁰²(103-digit number)

23055724890961584362…44049044756582707199

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

2.305 × 10¹⁰²(103-digit number)

23055724890961584362…44049044756582707199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.305 × 10¹⁰²(103-digit number)

23055724890961584362…44049044756582707201

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

4.611 × 10¹⁰²(103-digit number)

46111449781923168724…88098089513165414399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.611 × 10¹⁰²(103-digit number)

46111449781923168724…88098089513165414401

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

9.222 × 10¹⁰²(103-digit number)

92222899563846337448…76196179026330828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.222 × 10¹⁰²(103-digit number)

92222899563846337448…76196179026330828801

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

1.844 × 10¹⁰³(104-digit number)

18444579912769267489…52392358052661657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.844 × 10¹⁰³(104-digit number)

18444579912769267489…52392358052661657601

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

3.688 × 10¹⁰³(104-digit number)

36889159825538534979…04784716105323315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.688 × 10¹⁰³(104-digit number)

36889159825538534979…04784716105323315201

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 #368,290

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