Block #63,962

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 4:49:17 AM · Difficulty 8.9805 · 6,749,880 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0d6d3235e4defb05990e9d84ec3d05651b57e9ae79fea0c91d0cd09b183702f

View on Chainz ↗

Height

#63,962

Difficulty

8.980483

Transactions

Size

845 B

Version

Bits

08fb00ee

Nonce

Timestamp

7/19/2013, 4:49:17 AM

Confirmations

6,749,880

Mined by

⛏️ P2SHAaBZTNQJUZgQxX2f35JfNCWuGD98c9Xs6h

Merkle Root

9d187f51ba1a31e799a6e755dfd2ef4292f557aa99c99c524da823148d0599bc

Transactions (3)

Coinbase6d32f3c230e817…616aea16db9fc1

1 in → 1 out12.4000 XPM110 B

AaBZTNQJ…98c9Xs6h

8a036d8d50465f…ec1be421e14baa

3 in → 1 out38.9600 XPM488 B

ARV2GVKa…53MTXfMB

542152cdf5caa9…50b2ab0f963c5c

1 in → 1 out12.4200 XPM158 B

AMTDtLtG…R3NjQnLi

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.

2.020 × 10⁹³(94-digit number)

20203545086002293314…63278959039353646439

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

2.020 × 10⁹³(94-digit number)

20203545086002293314…63278959039353646439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.020 × 10⁹³(94-digit number)

20203545086002293314…63278959039353646441

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

4.040 × 10⁹³(94-digit number)

40407090172004586628…26557918078707292879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.040 × 10⁹³(94-digit number)

40407090172004586628…26557918078707292881

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

8.081 × 10⁹³(94-digit number)

80814180344009173256…53115836157414585759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.081 × 10⁹³(94-digit number)

80814180344009173256…53115836157414585761

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

1.616 × 10⁹⁴(95-digit number)

16162836068801834651…06231672314829171519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.616 × 10⁹⁴(95-digit number)

16162836068801834651…06231672314829171521

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

3.232 × 10⁹⁴(95-digit number)

32325672137603669302…12463344629658343039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.232 × 10⁹⁴(95-digit number)

32325672137603669302…12463344629658343041

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 #63,962

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