Block #236,938

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 6:28:38 PM · Difficulty 9.9488 · 6,606,887 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50c686acddfd7e2b0411b0a61a2f47fd9424f1112af942ba57ae7e261dcf8ae1

View on Chainz ↗

Height

#236,938

Difficulty

9.948768

Transactions

Size

2.11 KB

Version

Bits

09f2e27e

Nonce

40,708

Timestamp

10/31/2013, 6:28:38 PM

Confirmations

6,606,887

Mined by

⛏️ RrDAeJPhjEZAvbBfkcAecCYvZED8VdkNigEjN

Merkle Root

c6c8f27820187115490615fb850f1aefb9391a44189ba41e9a5793b5a65813be

Transactions (1)

Coinbasec6c8f278201871…5793b5a65813be

1 in → 59 out10.0600 XPM2.02 KB

AeJPhjEZ…dkNigEjN AbeUZSvK…ijGzuyjz ANuKx9Ke…wm7nrBRq Aaox8Rxx…XTyyJXVx AQtzUSwq…htAuF3yC

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.

6.745 × 10⁹⁴(95-digit number)

67454295411324287653…73387184251956874719

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

6.745 × 10⁹⁴(95-digit number)

67454295411324287653…73387184251956874719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.745 × 10⁹⁴(95-digit number)

67454295411324287653…73387184251956874721

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

1.349 × 10⁹⁵(96-digit number)

13490859082264857530…46774368503913749439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.349 × 10⁹⁵(96-digit number)

13490859082264857530…46774368503913749441

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

2.698 × 10⁹⁵(96-digit number)

26981718164529715061…93548737007827498879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.698 × 10⁹⁵(96-digit number)

26981718164529715061…93548737007827498881

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

5.396 × 10⁹⁵(96-digit number)

53963436329059430122…87097474015654997759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.396 × 10⁹⁵(96-digit number)

53963436329059430122…87097474015654997761

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

1.079 × 10⁹⁶(97-digit number)

10792687265811886024…74194948031309995519

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 #236,938

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