Block #578,323

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/5/2014, 11:21:26 PM · Difficulty 10.9683 · 6,226,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cfcd65b351b5ad6ccb0f7025f6551a2d4d14dd4c5054ff3248ac171f1699449f

View on Chainz ↗

Height

#578,323

Difficulty

10.968333

Transactions

Size

1.09 KB

Version

Bits

0af7e4a5

Nonce

1,930,256,864

Timestamp

6/5/2014, 11:21:26 PM

Confirmations

6,226,792

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bb32206e01ef930093db7119ad3ea1e4ecb3edd7790b2bc960cb3173e5a4f374

Transactions (5)

Coinbase6cb441baa60c87…d267e5e4a3615e

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

0db4f849ebed69…2b7a5557dd8cb6

1 in → 2 out6.6855 XPM226 B

AGdWVjRk…LFVsqCnK AVKoLD7W…4Yt9KMBN

2761465ab84adc…503f2c7f65166a

1 in → 2 out6.0671 XPM226 B

ANtuMciH…YcnWwvMG Abs1CTRR…uk6ieBYF

3e83dd84ba9516…e82872ccdde9d4

1 in → 2 out3.5290 XPM226 B

Ac8zvpJu…j2sZ8uxi AYz8XXeX…wUExhw54

bb302aaa7cd345…30b5f2fcde2325

1 in → 2 out6.5797 XPM227 B

AJRmd8Y5…Aho6vtav AQYfM6tR…wtD7VsKo

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.

8.489 × 10¹⁰¹(102-digit number)

84897219357079926061…10761870358527672319

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

8.489 × 10¹⁰¹(102-digit number)

84897219357079926061…10761870358527672319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.489 × 10¹⁰¹(102-digit number)

84897219357079926061…10761870358527672321

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

1.697 × 10¹⁰²(103-digit number)

16979443871415985212…21523740717055344639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.697 × 10¹⁰²(103-digit number)

16979443871415985212…21523740717055344641

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

3.395 × 10¹⁰²(103-digit number)

33958887742831970424…43047481434110689279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.395 × 10¹⁰²(103-digit number)

33958887742831970424…43047481434110689281

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

6.791 × 10¹⁰²(103-digit number)

67917775485663940848…86094962868221378559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.791 × 10¹⁰²(103-digit number)

67917775485663940848…86094962868221378561

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

1.358 × 10¹⁰³(104-digit number)

13583555097132788169…72189925736442757119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.358 × 10¹⁰³(104-digit number)

13583555097132788169…72189925736442757121

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