Block #1,354,567

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2015, 8:35:05 PM · Difficulty 10.8060 · 5,462,649 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5a3423f8d07b4cf93f5d3cc56ecc139ef41999e09e908f44bf7f0fdbcfcb94ee

View on Chainz ↗

Height

#1,354,567

Difficulty

10.806017

Transactions

Size

427 B

Version

Bits

0ace5728

Nonce

1,609,742,964

Timestamp

12/4/2015, 8:35:05 PM

Confirmations

5,462,649

Mined by

⛏️ P2SHAd1mmFvMsEJAGZRdeSrruYVi5YBzMDg21i

Merkle Root

8357273dc7be1d27488746b4d9e81a39041a571597bffeda7a8231f60b1c0be1

Transactions (2)

Coinbase78d0d4b4fff1a3…b596707b8e5af7

1 in → 1 out8.5600 XPM110 B

Ad1mmFvM…BzMDg21i

e8dce72bfd1071…34b0037fea2625

1 in → 2 out5.8220 XPM226 B

AcuM7XiJ…5uND8Jce AZhQ1err…Msomet8e

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.

9.468 × 10⁹⁷(98-digit number)

94688041324063356483…00269630011477196799

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

9.468 × 10⁹⁷(98-digit number)

94688041324063356483…00269630011477196799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.468 × 10⁹⁷(98-digit number)

94688041324063356483…00269630011477196801

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

1.893 × 10⁹⁸(99-digit number)

18937608264812671296…00539260022954393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.893 × 10⁹⁸(99-digit number)

18937608264812671296…00539260022954393601

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

3.787 × 10⁹⁸(99-digit number)

37875216529625342593…01078520045908787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.787 × 10⁹⁸(99-digit number)

37875216529625342593…01078520045908787201

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

7.575 × 10⁹⁸(99-digit number)

75750433059250685186…02157040091817574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.575 × 10⁹⁸(99-digit number)

75750433059250685186…02157040091817574401

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

1.515 × 10⁹⁹(100-digit number)

15150086611850137037…04314080183635148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.515 × 10⁹⁹(100-digit number)

15150086611850137037…04314080183635148801

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 #1,354,567

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