Block #603,547

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/27/2014, 3:42:54 AM · Difficulty 10.9112 · 6,212,799 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2633f253ab821dbd4bd35255e3ce9b1341f807c376be4f267e3baca54a952737

View on Chainz ↗

Height

#603,547

Difficulty

10.911240

Transactions

Size

12.87 KB

Version

Bits

0ae94706

Nonce

915,349,843

Timestamp

6/27/2014, 3:42:54 AM

Confirmations

6,212,799

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b41221833e0ed0a2aaae1deff09fc92b6c591adb3d5e2d767681b3c98f960f8f

Transactions (4)

Coinbase1a73e88b3b7c86…c410c2eb63161c

1 in → 1 out8.5400 XPM116 B

ANSXnLY2…Sd25TjkD

1c0d258e7a1b91…30a0cb1e3f6a31

84 in → 2 out29.0100 XPM12.22 KB

AGYfmt9J…pmNtW6e2 AaoEXkj5…Q8Nqode7

edd5d2e67a8dc9…8786d726877c7b

1 in → 2 out2.2719 XPM226 B

AerPNayq…WVniQyks Aa6m331p…NVBR9cYG

0766f62ed30b6d…aa2cd1d11e487f

1 in → 2 out2.2569 XPM226 B

AcAJHTWL…J8Cgemxi AKXkfMso…YLoTt7zi

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.

4.742 × 10¹⁰⁰(101-digit number)

47425574988037530356…13931528364844318719

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

4.742 × 10¹⁰⁰(101-digit number)

47425574988037530356…13931528364844318719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.742 × 10¹⁰⁰(101-digit number)

47425574988037530356…13931528364844318721

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

9.485 × 10¹⁰⁰(101-digit number)

94851149976075060713…27863056729688637439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.485 × 10¹⁰⁰(101-digit number)

94851149976075060713…27863056729688637441

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

1.897 × 10¹⁰¹(102-digit number)

18970229995215012142…55726113459377274879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.897 × 10¹⁰¹(102-digit number)

18970229995215012142…55726113459377274881

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

3.794 × 10¹⁰¹(102-digit number)

37940459990430024285…11452226918754549759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.794 × 10¹⁰¹(102-digit number)

37940459990430024285…11452226918754549761

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

7.588 × 10¹⁰¹(102-digit number)

75880919980860048570…22904453837509099519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.588 × 10¹⁰¹(102-digit number)

75880919980860048570…22904453837509099521

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 #603,547

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