Block #88,390

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 2:34:08 PM · Difficulty 9.2669 · 6,738,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f2e6e07419a6f0f0f0d6006d125ee9537082ae59f1196e24e21e901a5db4fb9e

View on Chainz ↗

Height

#88,390

Difficulty

9.266912

Transactions

Size

1021 B

Version

Bits

09445455

Nonce

6,759

Timestamp

7/29/2013, 2:34:08 PM

Confirmations

6,738,794

Mined by

⛏️ P2SHAWTVDp3WVGQJUCejCKbQGDxroLjWyVvijV

Merkle Root

afd34cc85f4fb85a923442fcc3d40e2677e9b19385f5b80ba3ed2a080a2cc328

Transactions (2)

Coinbaseee046e1dc0872a…b0733bd5526137

1 in → 1 out11.6400 XPM109 B

AWTVDp3W…jWyVvijV

38c994a123a6ad…3146adba790c5c

5 in → 2 out68.0010 XPM817 B

AdK1vS87…Ua6pLYG2 ASyS2w9Y…XjRz5HHz

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.

1.169 × 10¹⁰⁷(108-digit number)

11692138062420452267…51717177874067759329

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

1.169 × 10¹⁰⁷(108-digit number)

11692138062420452267…51717177874067759329

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.169 × 10¹⁰⁷(108-digit number)

11692138062420452267…51717177874067759331

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

2.338 × 10¹⁰⁷(108-digit number)

23384276124840904535…03434355748135518659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.338 × 10¹⁰⁷(108-digit number)

23384276124840904535…03434355748135518661

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

4.676 × 10¹⁰⁷(108-digit number)

46768552249681809070…06868711496271037319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.676 × 10¹⁰⁷(108-digit number)

46768552249681809070…06868711496271037321

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

9.353 × 10¹⁰⁷(108-digit number)

93537104499363618141…13737422992542074639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.353 × 10¹⁰⁷(108-digit number)

93537104499363618141…13737422992542074641

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

1.870 × 10¹⁰⁸(109-digit number)

18707420899872723628…27474845985084149279

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

Block #88,390

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