Block #510,990

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/25/2014, 11:27:05 PM · Difficulty 10.8284 · 6,306,901 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d562b009cc33108fdf8b06ef76fa38290577e3d3459682c420b48a126d878f88

View on Chainz ↗

Height

#510,990

Difficulty

10.828441

Transactions

Size

3.03 KB

Version

Bits

0ad414bb

Nonce

180,290

Timestamp

4/25/2014, 11:27:05 PM

Confirmations

6,306,901

Mined by

⛏️ aSZ#AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b6cc3f2acb9fd6a88b77582ce83f40408b1721c4137f4118ba192ec9cbc63084

Transactions (4)

Coinbasec6f42600ccd698…1813e12dd8ac13

1 in → 19 out8.5100 XPM709 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AQyr8Lw3…hs4nt3Pn

eedd068f0a978d…d591e5c6b4c5dd

12 in → 2 out103.4400 XPM1.81 KB

AGVgwCRv…2r9YbV5n AUUFsfr3…BUY1sWMK

056839d61035e4…b357839669e22f

1 in → 2 out8.5200 XPM225 B

AWwwmtRz…2t7rvSnr AN3mFVC8…3JEDoVbj

0b03528c0ff2e7…029cdaee633d21

1 in → 2 out8.5200 XPM226 B

AYWqnFYk…X86wW14p ARqjsjnD…FroVCN1r

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.

1.512 × 10⁹⁷(98-digit number)

15126408512012454273…76024007962753779199

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

1.512 × 10⁹⁷(98-digit number)

15126408512012454273…76024007962753779199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.512 × 10⁹⁷(98-digit number)

15126408512012454273…76024007962753779201

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

3.025 × 10⁹⁷(98-digit number)

30252817024024908547…52048015925507558399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.025 × 10⁹⁷(98-digit number)

30252817024024908547…52048015925507558401

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

6.050 × 10⁹⁷(98-digit number)

60505634048049817094…04096031851015116799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.050 × 10⁹⁷(98-digit number)

60505634048049817094…04096031851015116801

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

1.210 × 10⁹⁸(99-digit number)

12101126809609963418…08192063702030233599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.210 × 10⁹⁸(99-digit number)

12101126809609963418…08192063702030233601

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

2.420 × 10⁹⁸(99-digit number)

24202253619219926837…16384127404060467199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.420 × 10⁹⁸(99-digit number)

24202253619219926837…16384127404060467201

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

4.840 × 10⁹⁸(99-digit number)

48404507238439853675…32768254808120934399

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 #510,990

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