Block #63,701

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 3:08:25 AM · Difficulty 8.9798 · 6,741,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b60f7a0b8c272cd94a01cc98a0ec48381561878153f365c3bf65f5a8ffbf6f7

View on Chainz ↗

Height

#63,701

Difficulty

8.979841

Transactions

Size

1.13 KB

Version

Bits

08fad6dc

Nonce

1,077

Timestamp

7/19/2013, 3:08:25 AM

Confirmations

6,741,908

Mined by

⛏️ P2SHAVpGk3q8PHXaJqCaTV3HNvPJfx3tMZhgzZ

Merkle Root

4c3d894f023de3f9d42e227797c8b538126af68fd1c466fcd8832e63dd1fca8a

Transactions (2)

Coinbase05f6643df89966…09cd138bedef5d

1 in → 1 out12.4000 XPM109 B

AVpGk3q8…3tMZhgzZ

67eddaa027345e…97d2991f426d68

8 in → 1 out125.0000 XPM958 B

AGseYTRz…fHCkkwV7

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.

1.676 × 10¹⁰²(103-digit number)

16766305627451135179…77581125158940527999

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

1.676 × 10¹⁰²(103-digit number)

16766305627451135179…77581125158940527999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.676 × 10¹⁰²(103-digit number)

16766305627451135179…77581125158940528001

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

3.353 × 10¹⁰²(103-digit number)

33532611254902270358…55162250317881055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.353 × 10¹⁰²(103-digit number)

33532611254902270358…55162250317881056001

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

6.706 × 10¹⁰²(103-digit number)

67065222509804540716…10324500635762111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.706 × 10¹⁰²(103-digit number)

67065222509804540716…10324500635762112001

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

1.341 × 10¹⁰³(104-digit number)

13413044501960908143…20649001271524223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.341 × 10¹⁰³(104-digit number)

13413044501960908143…20649001271524224001

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

2.682 × 10¹⁰³(104-digit number)

26826089003921816286…41298002543048447999

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