Block #731,574

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/20/2014, 1:05:54 PM · Difficulty 10.9704 · 6,079,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af60a970f20db33fff8da1988c156d91a32aed86fa6474d54e273b3d1280832b

View on Chainz ↗

Height

#731,574

Difficulty

10.970414

Transactions

Size

434 B

Version

Bits

0af86d0f

Nonce

174,753,438

Timestamp

9/20/2014, 1:05:54 PM

Confirmations

6,079,444

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d853d240476657444dfca956ab0874761257fcec118ca4150b306ebbfa976979

Transactions (2)

Coinbase4ace4628e928fb…407c3db7205863

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

7ef78d25935f56…8bc647e074af2a

1 in → 2 out3.4767 XPM227 B

AeKNrjNj…1NEq95Ta ATXFZVYv…JduPzKNb

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.

5.031 × 10⁹⁷(98-digit number)

50319633520945583363…45272685081327831039

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

5.031 × 10⁹⁷(98-digit number)

50319633520945583363…45272685081327831039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.031 × 10⁹⁷(98-digit number)

50319633520945583363…45272685081327831041

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

1.006 × 10⁹⁸(99-digit number)

10063926704189116672…90545370162655662079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.006 × 10⁹⁸(99-digit number)

10063926704189116672…90545370162655662081

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

2.012 × 10⁹⁸(99-digit number)

20127853408378233345…81090740325311324159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.012 × 10⁹⁸(99-digit number)

20127853408378233345…81090740325311324161

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

4.025 × 10⁹⁸(99-digit number)

40255706816756466690…62181480650622648319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.025 × 10⁹⁸(99-digit number)

40255706816756466690…62181480650622648321

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

8.051 × 10⁹⁸(99-digit number)

80511413633512933381…24362961301245296639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.051 × 10⁹⁸(99-digit number)

80511413633512933381…24362961301245296641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.610 × 10⁹⁹(100-digit number)

16102282726702586676…48725922602490593279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #731,574

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