Block #196,476

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 12:33:17 PM · Difficulty 9.8809 · 6,628,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94f4093c594836207c700ddde22ef75c3ab898941c11523abf2d3c6e77c516eb

View on Chainz ↗

Height

#196,476

Difficulty

9.880912

Transactions

Size

356 B

Version

Bits

09e18373

Nonce

57,577

Timestamp

10/6/2013, 12:33:17 PM

Confirmations

6,628,652

Mined by

⛏️ P2SHASbwzPTTJ4Dogjio1ragQ3EydoXC3H7o8k

Merkle Root

885b409c382cc3d23b04c631d24e5b220007da498d452e6c05143a0fe02eddff

Transactions (2)

Coinbased048c599e800de…df5915b0e4269d

1 in → 1 out10.2400 XPM109 B

ASbwzPTT…XC3H7o8k

1c797cf7459bb2…35de1f215d0446

1 in → 1 out10.2300 XPM158 B

AKVZmjFY…iuD64V6a

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.

4.632 × 10⁹¹(92-digit number)

46324949042862787168…41835478188672625599

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

4.632 × 10⁹¹(92-digit number)

46324949042862787168…41835478188672625599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.632 × 10⁹¹(92-digit number)

46324949042862787168…41835478188672625601

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

9.264 × 10⁹¹(92-digit number)

92649898085725574336…83670956377345251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.264 × 10⁹¹(92-digit number)

92649898085725574336…83670956377345251201

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

1.852 × 10⁹²(93-digit number)

18529979617145114867…67341912754690502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.852 × 10⁹²(93-digit number)

18529979617145114867…67341912754690502401

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

3.705 × 10⁹²(93-digit number)

37059959234290229734…34683825509381004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.705 × 10⁹²(93-digit number)

37059959234290229734…34683825509381004801

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

7.411 × 10⁹²(93-digit number)

74119918468580459469…69367651018762009599

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 #196,476

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