Block #199,083

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 3:53:07 AM · Difficulty 9.8868 · 6,615,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

635bd3b1f394ec4ec705586262372ae6263fa7897b2f14215bbfdcc83fbb242e

View on Chainz ↗

Height

#199,083

Difficulty

9.886822

Transactions

Size

1.65 KB

Version

Bits

09e306c0

Nonce

68,841

Timestamp

10/8/2013, 3:53:07 AM

Confirmations

6,615,010

Mined by

⛏️ P2SHARYdjwHXs3EpqSkTm2ShcJdKH6wzD4SUcf

Merkle Root

a1ed266744bc67aeb59a444a2d5bdd04fb77f823e51623158569a83055ff9158

Transactions (3)

Coinbase3fc778bdc0c721…25e7b793dd9324

1 in → 1 out10.2500 XPM109 B

ARYdjwHX…wzD4SUcf

8eb63e283a00c8…fddd39d3397d0c

8 in → 2 out10.6794 XPM1.24 KB

ALpthvGg…D1g5z4CT AeXZFvUx…9B9p88Nf

1abae9bf05bfb5…adbddba4f40ea3

1 in → 2 out2.1975 XPM226 B

AHEqEPxj…q6UA1ZB3 ANsZYAZy…wSk4mkms

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.

3.939 × 10⁹³(94-digit number)

39399541740996750536…36891559339521282499

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

3.939 × 10⁹³(94-digit number)

39399541740996750536…36891559339521282499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.939 × 10⁹³(94-digit number)

39399541740996750536…36891559339521282501

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

7.879 × 10⁹³(94-digit number)

78799083481993501073…73783118679042564999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.879 × 10⁹³(94-digit number)

78799083481993501073…73783118679042565001

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

1.575 × 10⁹⁴(95-digit number)

15759816696398700214…47566237358085129999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.575 × 10⁹⁴(95-digit number)

15759816696398700214…47566237358085130001

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

3.151 × 10⁹⁴(95-digit number)

31519633392797400429…95132474716170259999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.151 × 10⁹⁴(95-digit number)

31519633392797400429…95132474716170260001

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

6.303 × 10⁹⁴(95-digit number)

63039266785594800859…90264949432340519999

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 #199,083

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