Block #83,557

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 5:56:26 AM · Difficulty 9.2673 · 6,709,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9cefef408f1b1c14ea93d0551763549626a9be44091630e371d2653d79e2ad50

View on Chainz ↗

Height

#83,557

Difficulty

9.267333

Transactions

Size

205 B

Version

Bits

09446fe8

Nonce

108,561

Timestamp

7/26/2013, 5:56:26 AM

Confirmations

6,709,025

Merkle Root

a37eef5ffbc43bc6acc1be3eb38f4d894066b6c8c7d1c3a2e8c22778c5419bd1

Transactions (1)

Coinbasea37eef5ffbc43b…c22778c5419bd1

1 in → 1 out11.6300 XPM109 B

AbmC177F…pomdGgdX

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.

3.637 × 10¹⁰⁸(109-digit number)

36374553743950814894…09446197970396963099

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

3.637 × 10¹⁰⁸(109-digit number)

36374553743950814894…09446197970396963099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.637 × 10¹⁰⁸(109-digit number)

36374553743950814894…09446197970396963101

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

7.274 × 10¹⁰⁸(109-digit number)

72749107487901629789…18892395940793926199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.274 × 10¹⁰⁸(109-digit number)

72749107487901629789…18892395940793926201

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

1.454 × 10¹⁰⁹(110-digit number)

14549821497580325957…37784791881587852399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.454 × 10¹⁰⁹(110-digit number)

14549821497580325957…37784791881587852401

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

2.909 × 10¹⁰⁹(110-digit number)

29099642995160651915…75569583763175704799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.909 × 10¹⁰⁹(110-digit number)

29099642995160651915…75569583763175704801

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

5.819 × 10¹⁰⁹(110-digit number)

58199285990321303831…51139167526351409599

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