Block #234,489

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 8:28:59 AM · Difficulty 9.9443 · 6,582,888 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0b7cf1f3e1064a89684d292b5295f06b9bb2d19bbb8c4e577fac5b09653014c

View on Chainz ↗

Height

#234,489

Difficulty

9.944330

Transactions

Size

1.80 KB

Version

Bits

09f1bfa0

Nonce

64,706

Timestamp

10/30/2013, 8:28:59 AM

Confirmations

6,582,888

Mined by

⛏️ P2SHAURgwpocX3sNV87FAiDPfXg2t3tUCxooKN

Merkle Root

d342d6d2e1541ade15788be367bb29c43c656dd211c40090b7597e73d0ac8db4

Transactions (5)

Coinbase6caebe4efb975b…d2b340b28d31e1

1 in → 1 out10.1400 XPM109 B

AURgwpoc…tUCxooKN

4256b26e974840…a071172e44b2f5

5 in → 2 out48.5017 XPM819 B

ALCAAzHE…mBF4AcmN AN7ZnJS4…uHpiPac9

35edb7b65dd9aa…9faa45c17e45f3

1 in → 2 out2.9760 XPM226 B

ATioik7H…bKu7K2dz AZSGEPhc…mjEiQz5X

501f563ee4c621…fc6d7903e2901f

1 in → 2 out2.8481 XPM226 B

AWBkqPMM…QnvK8aGb AK1aDcD5…zAEo5DAU

3d14ac77d65f84…2d0f70b2999895

2 in → 2 out2.5659 XPM375 B

AaHw4fbK…mNkdXaJH Aa2JA2Lk…R4Q3S5WK

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.

1.394 × 10⁹⁵(96-digit number)

13948921494629470921…20359320880860687039

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

1.394 × 10⁹⁵(96-digit number)

13948921494629470921…20359320880860687039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.394 × 10⁹⁵(96-digit number)

13948921494629470921…20359320880860687041

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

2.789 × 10⁹⁵(96-digit number)

27897842989258941842…40718641761721374079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.789 × 10⁹⁵(96-digit number)

27897842989258941842…40718641761721374081

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

5.579 × 10⁹⁵(96-digit number)

55795685978517883684…81437283523442748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.579 × 10⁹⁵(96-digit number)

55795685978517883684…81437283523442748161

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

1.115 × 10⁹⁶(97-digit number)

11159137195703576736…62874567046885496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.115 × 10⁹⁶(97-digit number)

11159137195703576736…62874567046885496321

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

2.231 × 10⁹⁶(97-digit number)

22318274391407153473…25749134093770992639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #234,489

Cookie Preferences