Block #356,518

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 7:28:43 PM · Difficulty 10.3791 · 6,456,465 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb79b38e1b2939cbe81dacadf40917476e495af84857cc2aaefe6ca4099ef733

View on Chainz ↗

Height

#356,518

Difficulty

10.379067

Transactions

Size

1.71 KB

Version

Bits

0a610a8e

Nonce

32,529

Timestamp

1/12/2014, 7:28:43 PM

Confirmations

6,456,465

Mined by

⛏️ paRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

9461d3a5de50775b32b463f9301f7ac3eaf6ce2ca2b6d60d4eddf3e9c8bc833f

Transactions (4)

Coinbase8af19a76e826b5…a97cd3942d9e4f

1 in → 27 out9.2700 XPM981 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 ARYJiGcH…7eaSxdkL Ac7TsAMG…2W5MRTA8 AKwqFUdz…D4jGNKFN

43dfd60e7c0122…72c75765a91651

1 in → 2 out8.3498 XPM226 B

AJ3Ex8Eq…CU3PNKgn ASLSayLy…xefJ4XFk

73bdcab29e51d4…e3c4ae711ebca0

1 in → 2 out7.3302 XPM225 B

AMtybrdE…TagstRS9 AXxp24rY…yi3yUFBu

e33f19d479a8a3…3f2dd327d07abe

1 in → 2 out7.3390 XPM226 B

AYVyegUo…88drMYWV AXrwHJzX…Wjq29NuC

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.

2.617 × 10⁹³(94-digit number)

26171044980037589561…46966858133080306849

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

2.617 × 10⁹³(94-digit number)

26171044980037589561…46966858133080306849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.617 × 10⁹³(94-digit number)

26171044980037589561…46966858133080306851

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

5.234 × 10⁹³(94-digit number)

52342089960075179123…93933716266160613699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.234 × 10⁹³(94-digit number)

52342089960075179123…93933716266160613701

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

1.046 × 10⁹⁴(95-digit number)

10468417992015035824…87867432532321227399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.046 × 10⁹⁴(95-digit number)

10468417992015035824…87867432532321227401

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

2.093 × 10⁹⁴(95-digit number)

20936835984030071649…75734865064642454799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.093 × 10⁹⁴(95-digit number)

20936835984030071649…75734865064642454801

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

4.187 × 10⁹⁴(95-digit number)

41873671968060143298…51469730129284909599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.187 × 10⁹⁴(95-digit number)

41873671968060143298…51469730129284909601

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 #356,518

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