Block #357,431

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 10:10:21 AM · Difficulty 10.3833 · 6,455,613 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6de100ed7c37ca0e5958364470d8af7d015f83e627c10a502f4e031629fd339f

View on Chainz ↗

Height

#357,431

Difficulty

10.383307

Transactions

Size

1.38 KB

Version

Bits

0a622060

Nonce

800,637

Timestamp

1/13/2014, 10:10:21 AM

Confirmations

6,455,613

Mined by

⛏️ 7taRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

ddda1ae6f521b37cd0d3c1d697e0694af709f31f9e0c1a69a309fd6b1e9e3510

Transactions (4)

Coinbase48c64352fedd6a…62aefbdfc75047

1 in → 19 out9.2600 XPM709 B

Aac9Hjdg…P4ktypc3 ANeHTs9o…oazVAG8Z APeshfYV…3PKcKMKH AQ8QAT3J…rCFKuVbR Ac7TsAMG…2W5MRTA8

231c9a8c17fbb6…6bd98407480e3e

1 in → 1 out9.4000 XPM158 B

AGTJYYfi…XDqVJk9h

78c7c040b424ce…9280a7a843aa91

1 in → 2 out8.3080 XPM227 B

AMsvU24M…GyM7Jf7v ASLGKenC…rVPZC967

1fcced7cf9922d…d4659de7da0b97

1 in → 2 out7.2732 XPM227 B

ASi4Z44i…ePY1E2Xy AVXATcvE…XPdccfzZ

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.

1.291 × 10⁹²(93-digit number)

12913099655130889383…60536231990408721479

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

1.291 × 10⁹²(93-digit number)

12913099655130889383…60536231990408721479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.291 × 10⁹²(93-digit number)

12913099655130889383…60536231990408721481

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

2.582 × 10⁹²(93-digit number)

25826199310261778767…21072463980817442959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.582 × 10⁹²(93-digit number)

25826199310261778767…21072463980817442961

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

5.165 × 10⁹²(93-digit number)

51652398620523557535…42144927961634885919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.165 × 10⁹²(93-digit number)

51652398620523557535…42144927961634885921

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

1.033 × 10⁹³(94-digit number)

10330479724104711507…84289855923269771839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.033 × 10⁹³(94-digit number)

10330479724104711507…84289855923269771841

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

2.066 × 10⁹³(94-digit number)

20660959448209423014…68579711846539543679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.066 × 10⁹³(94-digit number)

20660959448209423014…68579711846539543681

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 #357,431

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