Block #603,736

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/27/2014, 7:09:35 AM · Difficulty 10.9110 · 6,201,424 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5617eca1d5dc4a15cc5dd5364bff9447f3319bd040c4d6b9f6cbaf4a7ed0e448

View on Chainz ↗

Height

#603,736

Difficulty

10.910953

Transactions

Size

662 B

Version

Bits

0ae9343a

Nonce

124,718,886

Timestamp

6/27/2014, 7:09:35 AM

Confirmations

6,201,424

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

094db4047f4974f2639b5d0f18b6d0ef312af815a5fe6d7154e606f87bca0d6c

Transactions (3)

Coinbase08b06fc09c0d22…bb51fc0e6da573

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

d829bc54811ea1…c569808ce92f4d

1 in → 2 out4.2522 XPM227 B

AWzX2ti8…iNs63CYy AYRSmLLF…ZVXPW7k9

41ec4a1b455072…ec4e67bfbe06ab

1 in → 2 out4.1616 XPM226 B

AKSL57hp…3cMcGXTL AZb7yH9J…wfH3JDno

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.

5.585 × 10¹⁰⁰(101-digit number)

55854737038231304582…46649398943455805439

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

5.585 × 10¹⁰⁰(101-digit number)

55854737038231304582…46649398943455805439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.585 × 10¹⁰⁰(101-digit number)

55854737038231304582…46649398943455805441

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

1.117 × 10¹⁰¹(102-digit number)

11170947407646260916…93298797886911610879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.117 × 10¹⁰¹(102-digit number)

11170947407646260916…93298797886911610881

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

2.234 × 10¹⁰¹(102-digit number)

22341894815292521832…86597595773823221759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.234 × 10¹⁰¹(102-digit number)

22341894815292521832…86597595773823221761

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

4.468 × 10¹⁰¹(102-digit number)

44683789630585043665…73195191547646443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.468 × 10¹⁰¹(102-digit number)

44683789630585043665…73195191547646443521

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

8.936 × 10¹⁰¹(102-digit number)

89367579261170087331…46390383095292887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.936 × 10¹⁰¹(102-digit number)

89367579261170087331…46390383095292887041

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