Block #568,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2014, 1:13:29 PM · Difficulty 10.9650 · 6,258,677 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c90cc4c62a352874dfad23332736655f92077fc57ffc37bf9eb3f7fc87c4cc1d

View on Chainz ↗

Height

#568,622

Difficulty

10.965038

Transactions

Size

1.51 KB

Version

Bits

0af70cba

Nonce

3,071,229,082

Timestamp

5/30/2014, 1:13:29 PM

Confirmations

6,258,677

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a07684a23c2a75b93cc45ee96d65ff4131758edff7b41fe0bd9f3136939b5ecb

Transactions (3)

Coinbasecc5277e97ac017…c8d4a919de3451

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

afc8cd00f86156…1a3d1af32398f7

5 in → 2 out180.3422 XPM818 B

AUMASSVb…dU32FpCd AaxMKtZP…ZoCbHAxU

b6f2151220f6d7…715c00dab13476

3 in → 2 out5.0432 XPM523 B

AeMSkPHX…ab9U2pv6 AWFDBc5K…fbhhyyJF

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.

2.053 × 10⁹⁷(98-digit number)

20539852204661021436…85650679577211142159

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

2.053 × 10⁹⁷(98-digit number)

20539852204661021436…85650679577211142159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.053 × 10⁹⁷(98-digit number)

20539852204661021436…85650679577211142161

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

4.107 × 10⁹⁷(98-digit number)

41079704409322042873…71301359154422284319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.107 × 10⁹⁷(98-digit number)

41079704409322042873…71301359154422284321

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

8.215 × 10⁹⁷(98-digit number)

82159408818644085746…42602718308844568639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.215 × 10⁹⁷(98-digit number)

82159408818644085746…42602718308844568641

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

1.643 × 10⁹⁸(99-digit number)

16431881763728817149…85205436617689137279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.643 × 10⁹⁸(99-digit number)

16431881763728817149…85205436617689137281

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

3.286 × 10⁹⁸(99-digit number)

32863763527457634298…70410873235378274559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.286 × 10⁹⁸(99-digit number)

32863763527457634298…70410873235378274561

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 #568,622

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