Block #321,200

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 4:26:18 AM · Difficulty 10.1861 · 6,475,437 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e085866a19cbde3c667885f5bd85a4b8aae26b2d56d97d0d4860d207474e18cf

View on Chainz ↗

Height

#321,200

Difficulty

10.186132

Transactions

Size

5.41 KB

Version

Bits

0a2fa65b

Nonce

35,123

Timestamp

12/20/2013, 4:26:18 AM

Confirmations

6,475,437

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7610bf00748d20ab50a61bad24401dcbbaba91df302cdd128e5ccd78a4d05848

Transactions (3)

Coinbase46251c3b39ac20…27586a442122fc

1 in → 1 out9.6900 XPM110 B

AeKNrjNj…1NEq95Ta

42a88ca5200d58…b1412338353b17

34 in → 2 out200.2484 XPM4.99 KB

AZWz8xMr…QroUPP9k AWVdzUhV…m6KBmW3z

9ec73cf85a387b…2473459c3a411c

1 in → 2 out5.6371 XPM226 B

AX92U3Ej…9rSCvMVD AVboVs94…HhhoMpnQ

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.

4.663 × 10¹⁰³(104-digit number)

46638558397571410542…78337418404919639039

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

4.663 × 10¹⁰³(104-digit number)

46638558397571410542…78337418404919639039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.663 × 10¹⁰³(104-digit number)

46638558397571410542…78337418404919639041

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

9.327 × 10¹⁰³(104-digit number)

93277116795142821084…56674836809839278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.327 × 10¹⁰³(104-digit number)

93277116795142821084…56674836809839278081

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

1.865 × 10¹⁰⁴(105-digit number)

18655423359028564216…13349673619678556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.865 × 10¹⁰⁴(105-digit number)

18655423359028564216…13349673619678556161

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

3.731 × 10¹⁰⁴(105-digit number)

37310846718057128433…26699347239357112319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.731 × 10¹⁰⁴(105-digit number)

37310846718057128433…26699347239357112321

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

7.462 × 10¹⁰⁴(105-digit number)

74621693436114256867…53398694478714224639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.462 × 10¹⁰⁴(105-digit number)

74621693436114256867…53398694478714224641

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