Block #235,981

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 6:12:16 AM · Difficulty 9.9464 · 6,573,253 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e74c54d804b43d30da41b01f016ee57cd7ce34bf3cab6b3e296e7a894fbe062

View on Chainz ↗

Height

#235,981

Difficulty

9.946442

Transactions

Size

7.81 KB

Version

Bits

09f24a05

Nonce

38,574

Timestamp

10/31/2013, 6:12:16 AM

Confirmations

6,573,253

Mined by

⛏️ P2SHAHnBbSZUB33VknNc1hSqs87dGJRVfat6WW

Merkle Root

11ca9834da7c1320453338d4017306ee33dfe0ea78f423d53bd19dfa2d9ceaeb

Transactions (4)

Coinbase021a5e799ea52e…5ca72a36e8840f

1 in → 1 out10.1900 XPM109 B

AHnBbSZU…RVfat6WW

078e143372b51e…19cfb7200dc2c3

2 in → 2 out20.2000 XPM375 B

ALL6BtTJ…cp6j3qpk APybZSNb…NhQimY8D

9d7d908fefa25c…3f83c12e37a553

48 in → 2 out4.9100 XPM7.02 KB

AVh7oCT2…TKazDD84 AUUdEFhD…xxU7mgj5

8ea85ddc6e1377…166b0be6507ffe

1 in → 2 out2.9153 XPM226 B

AHCMBdHF…ZJLreTRk AXTD5Xo7…9JgpWu5d

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.

2.113 × 10¹⁰³(104-digit number)

21131222884334156506…18347963693114407049

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

2.113 × 10¹⁰³(104-digit number)

21131222884334156506…18347963693114407049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.113 × 10¹⁰³(104-digit number)

21131222884334156506…18347963693114407051

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

4.226 × 10¹⁰³(104-digit number)

42262445768668313013…36695927386228814099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.226 × 10¹⁰³(104-digit number)

42262445768668313013…36695927386228814101

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

8.452 × 10¹⁰³(104-digit number)

84524891537336626026…73391854772457628199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.452 × 10¹⁰³(104-digit number)

84524891537336626026…73391854772457628201

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

1.690 × 10¹⁰⁴(105-digit number)

16904978307467325205…46783709544915256399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.690 × 10¹⁰⁴(105-digit number)

16904978307467325205…46783709544915256401

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

3.380 × 10¹⁰⁴(105-digit number)

33809956614934650410…93567419089830512799

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 #235,981

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