Block #370,970

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/22/2014, 12:43:54 PM · Difficulty 10.4371 · 6,441,298 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f7f95a183227975b87fca1911153bf94ca29631d6716886f630fdb784f03f95

View on Chainz ↗

Height

#370,970

Difficulty

10.437135

Transactions

Size

1.66 KB

Version

Bits

0a6fe81b

Nonce

2,067,863

Timestamp

1/22/2014, 12:43:54 PM

Confirmations

6,441,298

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b8a6940e5ea28879764599037c90edbdb671faf7761d6d4a4b04d0f2bd5af839

Transactions (5)

Coinbase96fe19e057ede3…f285432ae67d47

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

9731cd719f4f95…3816ffa5e48c77

2 in → 2 out18.4400 XPM375 B

AJdvJmjS…GFTusQmv AM9hZNeN…8MwAwXpi

47ccc67169499d…bcad5b38fea456

2 in → 2 out18.4400 XPM375 B

ATZUp49D…xaoNMsmK ARR1Bdj3…8N2afAtZ

9d2a9b4a9e3d36…cb245fcd41e30d

2 in → 2 out18.4400 XPM372 B

AZgXbtCd…o9B9wgn4 AFreewNR…WwhUuhEf

0cc8ffd1d778c0…8e0f915eb5f467

2 in → 2 out18.4400 XPM375 B

AYMgMnW1…xZqEHDzD AJJu16ii…1zZTWnqc

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.

2.423 × 10⁹²(93-digit number)

24230290196998717445…00927843957925696599

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

2.423 × 10⁹²(93-digit number)

24230290196998717445…00927843957925696599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.423 × 10⁹²(93-digit number)

24230290196998717445…00927843957925696601

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

4.846 × 10⁹²(93-digit number)

48460580393997434891…01855687915851393199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.846 × 10⁹²(93-digit number)

48460580393997434891…01855687915851393201

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

9.692 × 10⁹²(93-digit number)

96921160787994869782…03711375831702786399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.692 × 10⁹²(93-digit number)

96921160787994869782…03711375831702786401

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

1.938 × 10⁹³(94-digit number)

19384232157598973956…07422751663405572799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.938 × 10⁹³(94-digit number)

19384232157598973956…07422751663405572801

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

3.876 × 10⁹³(94-digit number)

38768464315197947912…14845503326811145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.876 × 10⁹³(94-digit number)

38768464315197947912…14845503326811145601

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 #370,970

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