Block #357,869

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 4:36:59 PM · Difficulty 10.3894 · 6,437,087 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c98b0fc033fd262bebeb00270c8c38f7260a0efa30e427b7e190fa3b02d1832

View on Chainz ↗

Height

#357,869

Difficulty

10.389387

Transactions

Size

3.05 KB

Version

Bits

0a63aed8

Nonce

5,934

Timestamp

1/13/2014, 4:36:59 PM

Confirmations

6,437,087

Mined by

⛏️ uaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

94e6bae439da92adb8b8ecbfa86d3ccf618d4c5d5a82be14196aec15eaef5a4f

Transactions (4)

Coinbasec4d91098ed100d…55bd340384900e

1 in → 26 out9.2500 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AJzWx2VD…j4ZSMit5 Ac7TsAMG…2W5MRTA8

8055139b2d9d72…52ff7968620c16

2 in → 2 out13.3134 XPM372 B

AMtJhuBd…CXfiXRt1 AXNLYned…K36YScoR

6279dac9712ae9…109c69193b0eb0

7 in → 19 out57.9748 XPM1.46 KB

AHzK8Ygg…GcngkFzV AH8z3gEd…ENu7n9sN AZekxBFu…vTyGaSNV AHXxppsF…jkGkqokY APQCLq5D…cpNbYpoy

8636d9dd81beb0…0b1ddef2a675e2

1 in → 2 out7.1397 XPM225 B

AFreewNR…WwhUuhEf AGSwpB7y…NpojqwUY

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.

9.427 × 10⁹³(94-digit number)

94275026478503395903…42737970264905131439

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

9.427 × 10⁹³(94-digit number)

94275026478503395903…42737970264905131439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.427 × 10⁹³(94-digit number)

94275026478503395903…42737970264905131441

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

1.885 × 10⁹⁴(95-digit number)

18855005295700679180…85475940529810262879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.885 × 10⁹⁴(95-digit number)

18855005295700679180…85475940529810262881

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

3.771 × 10⁹⁴(95-digit number)

37710010591401358361…70951881059620525759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.771 × 10⁹⁴(95-digit number)

37710010591401358361…70951881059620525761

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

7.542 × 10⁹⁴(95-digit number)

75420021182802716722…41903762119241051519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.542 × 10⁹⁴(95-digit number)

75420021182802716722…41903762119241051521

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

1.508 × 10⁹⁵(96-digit number)

15084004236560543344…83807524238482103039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.508 × 10⁹⁵(96-digit number)

15084004236560543344…83807524238482103041

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