Block #423,853

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 5:31:19 PM · Difficulty 10.3770 · 6,382,158 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d20065aced84e83aed5ffaf34b88a03c928b3c39d143f47bc3bda88d9595a3e8

View on Chainz ↗

Height

#423,853

Difficulty

10.376987

Transactions

Size

1.28 KB

Version

Bits

0a60823c

Nonce

1,170,846,720

Timestamp

2/28/2014, 5:31:19 PM

Confirmations

6,382,158

Mined by

⛏️ wAdmLQqEBU14cQNNcCjBHmxcccGrW9AUmd9

Merkle Root

85f32c2227ae8da95da868f07296ec1bf3c3fe0123f0e11f11386484b7237f19

Transactions (4)

Coinbase5c907acfed4425…7ed5bc99f3ed15

1 in → 1 out9.3000 XPM89 B

AdmLQqEB…rW9AUmd9

50ea21541888b7…a3827df70c10c0

3 in → 2 out16.3805 XPM523 B

AWVVykHA…d3i5zp8M AUuKj98y…p8ek6x8M

150af4e189d7e8…7509ddeb17ce70

2 in → 2 out8.6278 XPM375 B

AZWtfkuN…wCzwffuG AWVVykHA…d3i5zp8M

edc1025586566c…5ab74625cd7ccc

1 in → 2 out0.9913 XPM227 B

AKQhTxEz…9rM7cPaG Af4w13LH…16NouMvW

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.

1.097 × 10¹¹¹(112-digit number)

10974133845419110163…57782784948124988949

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

1.097 × 10¹¹¹(112-digit number)

10974133845419110163…57782784948124988949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.097 × 10¹¹¹(112-digit number)

10974133845419110163…57782784948124988951

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

2.194 × 10¹¹¹(112-digit number)

21948267690838220327…15565569896249977899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.194 × 10¹¹¹(112-digit number)

21948267690838220327…15565569896249977901

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

4.389 × 10¹¹¹(112-digit number)

43896535381676440654…31131139792499955799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.389 × 10¹¹¹(112-digit number)

43896535381676440654…31131139792499955801

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

8.779 × 10¹¹¹(112-digit number)

87793070763352881309…62262279584999911599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.779 × 10¹¹¹(112-digit number)

87793070763352881309…62262279584999911601

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

1.755 × 10¹¹²(113-digit number)

17558614152670576261…24524559169999823199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.755 × 10¹¹²(113-digit number)

17558614152670576261…24524559169999823201

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