Block #347,968

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2014, 12:49:31 PM · Difficulty 10.2466 · 6,461,301 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5861b5a3b4947dc8d7815a033a59b944b849b1eb454bcf9e2c19a419b424c5c1

View on Chainz ↗

Height

#347,968

Difficulty

10.246615

Transactions

Size

210 B

Version

Bits

0a3f222d

Nonce

349,776

Timestamp

1/7/2014, 12:49:31 PM

Confirmations

6,461,301

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

2958c640456f733c737df465b9be2696e62759e71fe6b0e1279f3d8117ae7b0a

Transactions (1)

Coinbase2958c640456f73…9f3d8117ae7b0a

1 in → 1 out9.5100 XPM116 B

AbwWkWZt…kawDhufa

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.

7.482 × 10¹⁰³(104-digit number)

74823866467979470641…13138227279354013039

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

7.482 × 10¹⁰³(104-digit number)

74823866467979470641…13138227279354013039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.482 × 10¹⁰³(104-digit number)

74823866467979470641…13138227279354013041

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

1.496 × 10¹⁰⁴(105-digit number)

14964773293595894128…26276454558708026079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.496 × 10¹⁰⁴(105-digit number)

14964773293595894128…26276454558708026081

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

2.992 × 10¹⁰⁴(105-digit number)

29929546587191788256…52552909117416052159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.992 × 10¹⁰⁴(105-digit number)

29929546587191788256…52552909117416052161

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

5.985 × 10¹⁰⁴(105-digit number)

59859093174383576513…05105818234832104319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.985 × 10¹⁰⁴(105-digit number)

59859093174383576513…05105818234832104321

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

1.197 × 10¹⁰⁵(106-digit number)

11971818634876715302…10211636469664208639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.197 × 10¹⁰⁵(106-digit number)

11971818634876715302…10211636469664208641

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 #347,968

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