Block #421,859

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 8:24:30 AM · Difficulty 10.3758 · 6,373,478 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97cb84310eb7eb1d52b7090321e43403b7ca9b32501f1225f12f2237e35df1c5

View on Chainz ↗

Height

#421,859

Difficulty

10.375828

Transactions

Size

887 B

Version

Bits

0a603648

Nonce

2,401

Timestamp

2/27/2014, 8:24:30 AM

Confirmations

6,373,478

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

00f871b37882b84c8ae7d02a7b160b461aad91a2b3ca966837f41baf0b3ef337

Transactions (4)

Coinbase8e50a23bec4f22…8f5c519805d7f4

1 in → 1 out9.3000 XPM116 B

AbwWkWZt…kawDhufa

44bfb318a33e94…6b8f2d975f29d7

1 in → 2 out8.1783 XPM225 B

AXNVLKpH…GHdwoAxs AWXMVpB1…koeTndnt

8a318c5be171f3…ef09cfa2143980

1 in → 2 out7.1663 XPM226 B

AWhqddAm…5ggySXwy AWKDmCxg…Z3bzF32C

87d85bb2f75406…1739649486bdae

1 in → 2 out5.0912 XPM227 B

AKJmXTVz…RYBr9Rgk AFreewNR…WwhUuhEf

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.

7.201 × 10¹⁰⁰(101-digit number)

72019965808391603094…07151373708026321919

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

7.201 × 10¹⁰⁰(101-digit number)

72019965808391603094…07151373708026321919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.201 × 10¹⁰⁰(101-digit number)

72019965808391603094…07151373708026321921

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

1.440 × 10¹⁰¹(102-digit number)

14403993161678320618…14302747416052643839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.440 × 10¹⁰¹(102-digit number)

14403993161678320618…14302747416052643841

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

2.880 × 10¹⁰¹(102-digit number)

28807986323356641237…28605494832105287679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.880 × 10¹⁰¹(102-digit number)

28807986323356641237…28605494832105287681

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

5.761 × 10¹⁰¹(102-digit number)

57615972646713282475…57210989664210575359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.761 × 10¹⁰¹(102-digit number)

57615972646713282475…57210989664210575361

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

1.152 × 10¹⁰²(103-digit number)

11523194529342656495…14421979328421150719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.152 × 10¹⁰²(103-digit number)

11523194529342656495…14421979328421150721

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