Block #601,230

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2014, 9:07:31 AM · Difficulty 10.9153 · 6,203,944 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3b62847adc2461b5fbb82a0f13ad3982ff47f1eb1b29aef147039fa255b82789

View on Chainz ↗

Height

#601,230

Difficulty

10.915270

Transactions

Size

886 B

Version

Bits

0aea4f21

Nonce

1,098,916,831

Timestamp

6/25/2014, 9:07:31 AM

Confirmations

6,203,944

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f2e028ead3a32d4ab3fc2bf2d79ce13dc22162de2c3a43e503c6c1084a4bc28e

Transactions (4)

Coinbase380985734cf9fd…06327e0e19addb

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

701580c1318086…0c758db923849d

1 in → 2 out4.4203 XPM226 B

AVQJezHF…aoz7LQWG AKXkfMso…YLoTt7zi

2b1dff5c0c3cc6…d21f662380c2da

1 in → 2 out3.1966 XPM226 B

AS9ZCvju…bu3NEFwZ AH3i5pWx…32oMd4HX

b474c376b4722c…43cad16ee8e682

1 in → 2 out3.3150 XPM227 B

ANaBE8Eq…h55XJP4X AWehni14…L1m7zv52

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.

4.703 × 10⁹⁷(98-digit number)

47037367133725508364…14356285643843358599

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

4.703 × 10⁹⁷(98-digit number)

47037367133725508364…14356285643843358599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.703 × 10⁹⁷(98-digit number)

47037367133725508364…14356285643843358601

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

9.407 × 10⁹⁷(98-digit number)

94074734267451016729…28712571287686717199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.407 × 10⁹⁷(98-digit number)

94074734267451016729…28712571287686717201

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

1.881 × 10⁹⁸(99-digit number)

18814946853490203345…57425142575373434399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.881 × 10⁹⁸(99-digit number)

18814946853490203345…57425142575373434401

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

3.762 × 10⁹⁸(99-digit number)

37629893706980406691…14850285150746868799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.762 × 10⁹⁸(99-digit number)

37629893706980406691…14850285150746868801

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

7.525 × 10⁹⁸(99-digit number)

75259787413960813383…29700570301493737599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.525 × 10⁹⁸(99-digit number)

75259787413960813383…29700570301493737601

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