Block #59,358

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 1:38:29 AM · Difficulty 8.9646 · 6,730,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2614f66976cdd97b96d5d52fe18e5a74991c20879970dfe8ce3c9f847902bfba

View on Chainz ↗

Height

#59,358

Difficulty

8.964586

Transactions

Size

200 B

Version

Bits

08f6ef1f

Nonce

253

Timestamp

7/18/2013, 1:38:29 AM

Confirmations

6,730,700

Merkle Root

cecf6fe36df5d7d05c22c8f11795ac56cb018ed8c23b7f1c716364ea63cff3e4

Transactions (1)

Coinbasececf6fe36df5d7…6364ea63cff3e4

1 in → 1 out12.4300 XPM110 B

AeTcmmqH…LrFchfe1

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.

8.836 × 10⁹⁴(95-digit number)

88360277434985338747…75784055842397732419

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

8.836 × 10⁹⁴(95-digit number)

88360277434985338747…75784055842397732419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.836 × 10⁹⁴(95-digit number)

88360277434985338747…75784055842397732421

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

1.767 × 10⁹⁵(96-digit number)

17672055486997067749…51568111684795464839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.767 × 10⁹⁵(96-digit number)

17672055486997067749…51568111684795464841

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

3.534 × 10⁹⁵(96-digit number)

35344110973994135499…03136223369590929679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.534 × 10⁹⁵(96-digit number)

35344110973994135499…03136223369590929681

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

7.068 × 10⁹⁵(96-digit number)

70688221947988270998…06272446739181859359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.068 × 10⁹⁵(96-digit number)

70688221947988270998…06272446739181859361

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

1.413 × 10⁹⁶(97-digit number)

14137644389597654199…12544893478363718719

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