Block #258,954

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 8:46:40 AM · Difficulty 9.9768 · 6,566,356 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba36c4a3aff954e63b09f22be23dc05c6ff829c263b2d7a6b53e86721f5ec311

View on Chainz ↗

Height

#258,954

Difficulty

9.976839

Transactions

Size

1.95 KB

Version

Bits

09fa1218

Nonce

6,003

Timestamp

11/13/2013, 8:46:40 AM

Confirmations

6,566,356

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

54ce320ff475b5d67454dc4e9af9d5b16da469df84ed441176ae893f6604da5b

Transactions (5)

Coinbase58e629b5c67a65…b37868e85f9171

1 in → 2 out10.0700 XPM136 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

f4a4c2cfcd949f…ae0e9c81f83031

1 in → 4 out13.9875 XPM295 B

AGZXqk7G…2xqXnQB9 AUAjjeWc…gzysQzwJ Adu2tcry…8NcZQscX AKwH2FW6…tCTn4qze

fbf12334959279…b82b109961abb8

1 in → 4 out12.2375 XPM293 B

AUAjjeWc…gzysQzwJ Adu2tcry…8NcZQscX AKwH2FW6…tCTn4qze AQ4QFqTZ…YFBrCoxe

2d40ad785e2e80…14a6fc398a66a0

1 in → 4 out17.9500 XPM295 B

AKN8Fr29…jE1F3shL AUAjjeWc…gzysQzwJ Adu2tcry…8NcZQscX AKwH2FW6…tCTn4qze

f8a09ad0afe9d8…0a6d5ba0e7b092

5 in → 4 out6.0149 XPM886 B

AKwH2FW6…tCTn4qze AZt7pgDY…UJ2JKX3y Adu2tcry…8NcZQscX AUAjjeWc…gzysQzwJ

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.

2.641 × 10⁹⁶(97-digit number)

26418358069578072025…70978315584065247999

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

2.641 × 10⁹⁶(97-digit number)

26418358069578072025…70978315584065247999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.641 × 10⁹⁶(97-digit number)

26418358069578072025…70978315584065248001

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

5.283 × 10⁹⁶(97-digit number)

52836716139156144050…41956631168130495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.283 × 10⁹⁶(97-digit number)

52836716139156144050…41956631168130496001

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

1.056 × 10⁹⁷(98-digit number)

10567343227831228810…83913262336260991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.056 × 10⁹⁷(98-digit number)

10567343227831228810…83913262336260992001

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

2.113 × 10⁹⁷(98-digit number)

21134686455662457620…67826524672521983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.113 × 10⁹⁷(98-digit number)

21134686455662457620…67826524672521984001

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

4.226 × 10⁹⁷(98-digit number)

42269372911324915240…35653049345043967999

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 #258,954

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