Block #352,400

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 7:46:37 AM · Difficulty 10.3073 · 6,452,961 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

51b37eb8652f231e37b1c1d21bbe811ba83a9bdccfe4db4e67d197f0deb1a890

View on Chainz ↗

Height

#352,400

Difficulty

10.307281

Transactions

Size

2.93 KB

Version

Bits

0a4ea9fa

Nonce

140,497

Timestamp

1/10/2014, 7:46:37 AM

Confirmations

6,452,961

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9ddf2e0f2d00365d9d7db12ee9a612cadc0daefc3ed807357cd8af83b18ce0b4

Transactions (5)

Coinbase8410167f087f02…e5d59e7ead07b0

1 in → 1 out9.4600 XPM110 B

AeKNrjNj…1NEq95Ta

3d9e58ffa4f887…50a32b065654e2

9 in → 21 out68.9961 XPM1.78 KB

AUm83Bxb…uyw1H8FW AQTU33Aj…LynJxcjH AMU2ZXdL…xNXSfu6G ALbsahdd…Ky1eBXP3 AYJq4YVd…sPb3dC2v

4f28982bb1782b…06108b2d90f619

1 in → 2 out5.3358 XPM226 B

APXYNhHf…eG8Puujs APG9Nqgk…SGZFLyd7

97fd3ce171ccc9…65d3a6e5b08333

1 in → 2 out2.3794 XPM226 B

AVJRvnH7…3RRGN3SF AW3ht6eN…f9gR8Hi4

0eb954f15325b1…defba700455c42

3 in → 2 out1.0938 XPM521 B

Ab6vNpvc…DGvFVPrE AergFsQB…UhLUx8bt

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.

1.661 × 10¹⁰¹(102-digit number)

16611618024104075504…87287229286423859199

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

1.661 × 10¹⁰¹(102-digit number)

16611618024104075504…87287229286423859199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.661 × 10¹⁰¹(102-digit number)

16611618024104075504…87287229286423859201

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

3.322 × 10¹⁰¹(102-digit number)

33223236048208151009…74574458572847718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.322 × 10¹⁰¹(102-digit number)

33223236048208151009…74574458572847718401

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

6.644 × 10¹⁰¹(102-digit number)

66446472096416302018…49148917145695436799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.644 × 10¹⁰¹(102-digit number)

66446472096416302018…49148917145695436801

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

1.328 × 10¹⁰²(103-digit number)

13289294419283260403…98297834291390873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.328 × 10¹⁰²(103-digit number)

13289294419283260403…98297834291390873601

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

2.657 × 10¹⁰²(103-digit number)

26578588838566520807…96595668582781747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.657 × 10¹⁰²(103-digit number)

26578588838566520807…96595668582781747201

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