Block #62,960

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 10:30:17 PM · Difficulty 8.9779 · 6,728,032 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63f6a126efa218cbfc03a07e03109ae3a12658011eae50e0c186f297a4a1f0ef

View on Chainz ↗

Height

#62,960

Difficulty

8.977881

Transactions

Size

728 B

Version

Bits

08fa5668

Nonce

715

Timestamp

7/18/2013, 10:30:17 PM

Confirmations

6,728,032

Merkle Root

a05355174d643d9ccba63a2a9edd60c67fc7dbfabf4b74bb2df01a19f65ae19a

Transactions (2)

Coinbase6106ad039f24e6…67af7ee7e5075b

1 in → 1 out12.4000 XPM110 B

AcjuZf3F…a7FXDdyx

cfe6f0ef4465fa…012fc360201ff5

3 in → 2 out532.3333 XPM523 B

AJwYbbwh…B8Php2bA AcU3G17t…7wPGLC6Z

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.

6.915 × 10¹⁰⁵(106-digit number)

69150816590917454862…37457727365420838759

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

6.915 × 10¹⁰⁵(106-digit number)

69150816590917454862…37457727365420838759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.915 × 10¹⁰⁵(106-digit number)

69150816590917454862…37457727365420838761

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

1.383 × 10¹⁰⁶(107-digit number)

13830163318183490972…74915454730841677519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.383 × 10¹⁰⁶(107-digit number)

13830163318183490972…74915454730841677521

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

2.766 × 10¹⁰⁶(107-digit number)

27660326636366981944…49830909461683355039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.766 × 10¹⁰⁶(107-digit number)

27660326636366981944…49830909461683355041

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

5.532 × 10¹⁰⁶(107-digit number)

55320653272733963889…99661818923366710079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.532 × 10¹⁰⁶(107-digit number)

55320653272733963889…99661818923366710081

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

1.106 × 10¹⁰⁷(108-digit number)

11064130654546792777…99323637846733420159

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