Block #2,020,664

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2017, 3:01:56 AM · Difficulty 10.7144 · 4,810,204 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

588336b0b3de6bf19659fd7f3170f37946f00b763cdde874c6667478cec9922c

View on Chainz ↗

Height

#2,020,664

Difficulty

10.714352

Transactions

Size

574 B

Version

Bits

0ab6dfc4

Nonce

602,512,097

Timestamp

3/13/2017, 3:01:56 AM

Confirmations

4,810,204

Mined by

⛏️ P2SHAJZkUkEpALB9h41jnGctWNYRpkdCsX5Aa2

Merkle Root

42f9c68e244f542d0a36bcca9a4102abd68a34f3914abdfe15ca0067c9339d20

Transactions (2)

Coinbase10d5b5d236abe5…e39c3f1a471762

1 in → 1 out8.7100 XPM110 B

AJZkUkEp…dCsX5Aa2

2602fc1f17c4a6…a3ee7e61ea084b

2 in → 2 out0.4787 XPM374 B

APhjT6aE…rmbdyPLJ AenLqRHS…E6MPf64X

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.

1.223 × 10⁹⁴(95-digit number)

12230576258498293748…16960640831708796159

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

1.223 × 10⁹⁴(95-digit number)

12230576258498293748…16960640831708796159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.223 × 10⁹⁴(95-digit number)

12230576258498293748…16960640831708796161

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

2.446 × 10⁹⁴(95-digit number)

24461152516996587497…33921281663417592319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.446 × 10⁹⁴(95-digit number)

24461152516996587497…33921281663417592321

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

4.892 × 10⁹⁴(95-digit number)

48922305033993174994…67842563326835184639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.892 × 10⁹⁴(95-digit number)

48922305033993174994…67842563326835184641

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

9.784 × 10⁹⁴(95-digit number)

97844610067986349989…35685126653670369279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.784 × 10⁹⁴(95-digit number)

97844610067986349989…35685126653670369281

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

1.956 × 10⁹⁵(96-digit number)

19568922013597269997…71370253307340738559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.956 × 10⁹⁵(96-digit number)

19568922013597269997…71370253307340738561

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 #2,020,664

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