Block #79,688

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 4:13:31 PM · Difficulty 9.2433 · 6,711,912 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2b62fecdf3f78fd515ea3875f43c31ff19fdb8386ee35587b9b0851d5b08919

View on Chainz ↗

Height

#79,688

Difficulty

9.243324

Transactions

Size

1.60 KB

Version

Bits

093e4a79

Nonce

650

Timestamp

7/23/2013, 4:13:31 PM

Confirmations

6,711,912

Merkle Root

dc65553651f3142be45dfa636eb6caf77d60a37045e32a4f53b0d57fa8a375fb

Transactions (5)

Coinbase1319f1c0a7ed86…0a9c617d311dac

1 in → 1 out11.7300 XPM110 B

AbmC177F…pomdGgdX

a81b9f6d517477…81b4aa99eda3ec

4 in → 2 out199.3174 XPM670 B

AR7akR6p…4mV7ALHt APgixiXf…r3YobDzq

758714ef2de10b…343e1007863a66

3 in → 1 out41.0200 XPM384 B

AeAKTaLB…zhPHFiXU

cf361d1f8310b8…d4dda3c75feb5c

1 in → 1 out12.1000 XPM157 B

ANHU6bZQ…RL9ELcPW

28ae5ea965d532…45b5c5c75c2ede

1 in → 2 out6.3200 XPM227 B

AKKgEbjp…77CibvvY AduFHScr…VSWpBhRA

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.

2.079 × 10⁹⁶(97-digit number)

20795629636721873803…45201241457388963459

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

2.079 × 10⁹⁶(97-digit number)

20795629636721873803…45201241457388963459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.079 × 10⁹⁶(97-digit number)

20795629636721873803…45201241457388963461

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

4.159 × 10⁹⁶(97-digit number)

41591259273443747606…90402482914777926919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.159 × 10⁹⁶(97-digit number)

41591259273443747606…90402482914777926921

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

8.318 × 10⁹⁶(97-digit number)

83182518546887495213…80804965829555853839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.318 × 10⁹⁶(97-digit number)

83182518546887495213…80804965829555853841

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

1.663 × 10⁹⁷(98-digit number)

16636503709377499042…61609931659111707679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.663 × 10⁹⁷(98-digit number)

16636503709377499042…61609931659111707681

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

3.327 × 10⁹⁷(98-digit number)

33273007418754998085…23219863318223415359

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