Block #1,430,807

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/27/2016, 2:06:12 PM · Difficulty 10.7607 · 5,395,814 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fd3057c3ce56a1da38cb951aab9a3a4b47af7be14a30b738079c3acf4358de7

View on Chainz ↗

Height

#1,430,807

Difficulty

10.760714

Transactions

Size

2.26 KB

Version

Bits

0ac2be2f

Nonce

632,033,737

Timestamp

1/27/2016, 2:06:12 PM

Confirmations

5,395,814

Mined by

⛏️ P2SHAc1t8tBhq1SkRov7tNzex9Akmm48jfxWi3

Merkle Root

721f336a8ec2151a6e13c8c97151362c73e16431bd1ae3d8dbbeb4df19df4c5f

Transactions (4)

Coinbase3b184156dbe166…a1bd8614b36020

1 in → 1 out8.6500 XPM110 B

Ac1t8tBh…48jfxWi3

97534b0ef0b6bb…04e4f9bca9fad1

1 in → 18 out183.9785 XPM770 B

AMUNGo6F…Vri5Jq9Y ANT6FYei…mwuM7Nif AWJrs8nM…cjZTky2Y AXLkjH6Q…9wXKhR9V AYYjwVgu…Y96Hektf

901954118e4ce5…5d0db4e50d33f3

2 in → 2 out4.4400 XPM374 B

AYFVayqC…FwPanPub AKBo83mz…D18PoRsU

273702474d2750…ffda9da73f0620

6 in → 2 out4.3800 XPM967 B

AHjv1d8n…7QbSphXW AJy5tPBu…3ToDsASX

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.

2.169 × 10⁹⁴(95-digit number)

21693454792663822236…85796796979184893279

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

2.169 × 10⁹⁴(95-digit number)

21693454792663822236…85796796979184893279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.169 × 10⁹⁴(95-digit number)

21693454792663822236…85796796979184893281

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

4.338 × 10⁹⁴(95-digit number)

43386909585327644473…71593593958369786559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.338 × 10⁹⁴(95-digit number)

43386909585327644473…71593593958369786561

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

8.677 × 10⁹⁴(95-digit number)

86773819170655288946…43187187916739573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.677 × 10⁹⁴(95-digit number)

86773819170655288946…43187187916739573121

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

1.735 × 10⁹⁵(96-digit number)

17354763834131057789…86374375833479146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.735 × 10⁹⁵(96-digit number)

17354763834131057789…86374375833479146241

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

3.470 × 10⁹⁵(96-digit number)

34709527668262115578…72748751666958292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.470 × 10⁹⁵(96-digit number)

34709527668262115578…72748751666958292481

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

6.941 × 10⁹⁵(96-digit number)

69419055336524231156…45497503333916584959

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 #1,430,807

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