Block #357,719

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 2:34:49 PM · Difficulty 10.3859 · 6,438,005 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a96f23580c69ee8aa559dadeb0ae640b4aaf28c2cc58ed6db8ad7aee51b9f08

View on Chainz ↗

Height

#357,719

Difficulty

10.385892

Transactions

Size

6.92 KB

Version

Bits

0a62c9d6

Nonce

4,707

Timestamp

1/13/2014, 2:34:49 PM

Confirmations

6,438,005

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

32e0083d56f7ee9009fb8679c327cd668461ec75cdc7f0aafda293a096879b65

Transactions (2)

Coinbase4b4e7b587be4b4…237f6b29fa386e

1 in → 1 out9.3300 XPM116 B

AbwWkWZt…kawDhufa

ec181e1311b387…04ad9d42a729d1

46 in → 2 out10000.0100 XPM6.72 KB

AJUYdjty…N1Sa6EL1 Ae5WFHbn…gBo7rvHr

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.

2.754 × 10⁹⁵(96-digit number)

27543395376085685153…18765337325339036719

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

2.754 × 10⁹⁵(96-digit number)

27543395376085685153…18765337325339036719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.754 × 10⁹⁵(96-digit number)

27543395376085685153…18765337325339036721

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

5.508 × 10⁹⁵(96-digit number)

55086790752171370306…37530674650678073439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.508 × 10⁹⁵(96-digit number)

55086790752171370306…37530674650678073441

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

1.101 × 10⁹⁶(97-digit number)

11017358150434274061…75061349301356146879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.101 × 10⁹⁶(97-digit number)

11017358150434274061…75061349301356146881

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

2.203 × 10⁹⁶(97-digit number)

22034716300868548122…50122698602712293759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.203 × 10⁹⁶(97-digit number)

22034716300868548122…50122698602712293761

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

4.406 × 10⁹⁶(97-digit number)

44069432601737096245…00245397205424587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.406 × 10⁹⁶(97-digit number)

44069432601737096245…00245397205424587521

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