Block #356,817

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 11:57:42 PM · Difficulty 10.3828 · 6,446,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68590e774699e014758d23291848e3f2b392feca6ca20fa54259fbd4d28de9c6

View on Chainz ↗

Height

#356,817

Difficulty

10.382782

Transactions

Size

903 B

Version

Bits

0a61fe07

Nonce

29,704

Timestamp

1/12/2014, 11:57:42 PM

Confirmations

6,446,571

Mined by

⛏️ P2SHATMvbTn7mxK2vEXEy5suSfdoWDkQwXgts5

Merkle Root

0b2210455998c61680ef4b728c99bdd531c0a492f866320636c1e217a4abfd70

Transactions (3)

Coinbase6cff2bb73bd38d…499b311d8d1b78

1 in → 1 out9.2900 XPM109 B

ATMvbTn7…kQwXgts5

d197f5de6b0ec1…54057079976f45

2 in → 7 out18.9400 XPM475 B

AVEwhk4E…hksMzGvJ AbL5KvSy…ZJDwC2mn AYQHTd7a…9asrQc1E AeKNrjNj…1NEq95Ta AL2v7PE7…5Q5y9E81

49b9cf0731a77d…9a2dcbfcbf17d7

1 in → 2 out3.1600 XPM226 B

AQj3Cbwb…jsXm3LD5 AXvPypqS…NYWP4i9s

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.

2.095 × 10¹⁰²(103-digit number)

20955763249433470827…33451321771591585279

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

2.095 × 10¹⁰²(103-digit number)

20955763249433470827…33451321771591585279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.095 × 10¹⁰²(103-digit number)

20955763249433470827…33451321771591585281

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

4.191 × 10¹⁰²(103-digit number)

41911526498866941655…66902643543183170559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.191 × 10¹⁰²(103-digit number)

41911526498866941655…66902643543183170561

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

8.382 × 10¹⁰²(103-digit number)

83823052997733883311…33805287086366341119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.382 × 10¹⁰²(103-digit number)

83823052997733883311…33805287086366341121

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

1.676 × 10¹⁰³(104-digit number)

16764610599546776662…67610574172732682239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.676 × 10¹⁰³(104-digit number)

16764610599546776662…67610574172732682241

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

3.352 × 10¹⁰³(104-digit number)

33529221199093553324…35221148345465364479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.352 × 10¹⁰³(104-digit number)

33529221199093553324…35221148345465364481

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