Block #69,742

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 10:16:37 AM · Difficulty 8.9913 · 6,721,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0b5b588383a549b67cfac4a49242473040e068955d89d2eca2dec81d4eec1e3

View on Chainz ↗

Height

#69,742

Difficulty

8.991318

Transactions

Size

208 B

Version

Bits

08fdc6ff

Nonce

411

Timestamp

7/20/2013, 10:16:37 AM

Confirmations

6,721,482

Merkle Root

3089738e3e185a1bf752f5b47bef9a97468f467407a958a1385c89e5a48a3a52

Transactions (1)

Coinbase3089738e3e185a…5c89e5a48a3a52

1 in → 1 out12.3500 XPM109 B

AXSFye4r…ADf1YWCU

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.

8.813 × 10¹¹⁶(117-digit number)

88139540087454857249…57144460500988435339

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

8.813 × 10¹¹⁶(117-digit number)

88139540087454857249…57144460500988435339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.813 × 10¹¹⁶(117-digit number)

88139540087454857249…57144460500988435341

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

1.762 × 10¹¹⁷(118-digit number)

17627908017490971449…14288921001976870679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.762 × 10¹¹⁷(118-digit number)

17627908017490971449…14288921001976870681

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

3.525 × 10¹¹⁷(118-digit number)

35255816034981942899…28577842003953741359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.525 × 10¹¹⁷(118-digit number)

35255816034981942899…28577842003953741361

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

7.051 × 10¹¹⁷(118-digit number)

70511632069963885799…57155684007907482719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.051 × 10¹¹⁷(118-digit number)

70511632069963885799…57155684007907482721

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

1.410 × 10¹¹⁸(119-digit number)

14102326413992777159…14311368015814965439

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