Block #56,955

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 11:17:31 AM · Difficulty 8.9518 · 6,751,672 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc23c49838ce4a1fd076b26f5b168c2d541cc32bbfd2670d105cf77fc51298a4

View on Chainz ↗

Height

#56,955

Difficulty

8.951827

Transactions

Size

734 B

Version

Bits

08f3aae7

Nonce

237

Timestamp

7/17/2013, 11:17:31 AM

Confirmations

6,751,672

Mined by

⛏️ P2SHATQdHM438HCZHDfV6Cp6DWxTBBekCt9L6F

Merkle Root

bbc3c2a6bca811859d38eb220043354f6996ce0bd627c3fb9492e31778ab240c

Transactions (3)

Coinbase01421d38090a77…12772dd0aaf171

1 in → 1 out12.4800 XPM110 B

ATQdHM43…ekCt9L6F

6d77a0c97eb7d1…ffd65e4d89f1a6

2 in → 2 out90.8837 XPM375 B

AWeWcPM1…BA2a8s16 AbNa2n5e…XPW5MsGG

af82da253216bf…ed67af9147ae95

1 in → 1 out12.5700 XPM158 B

AG7dvNsQ…8mYEdta9

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.

2.587 × 10⁹⁶(97-digit number)

25873529959434905251…20035417354635175399

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

2.587 × 10⁹⁶(97-digit number)

25873529959434905251…20035417354635175399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.587 × 10⁹⁶(97-digit number)

25873529959434905251…20035417354635175401

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

5.174 × 10⁹⁶(97-digit number)

51747059918869810503…40070834709270350799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.174 × 10⁹⁶(97-digit number)

51747059918869810503…40070834709270350801

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

1.034 × 10⁹⁷(98-digit number)

10349411983773962100…80141669418540701599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.034 × 10⁹⁷(98-digit number)

10349411983773962100…80141669418540701601

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

2.069 × 10⁹⁷(98-digit number)

20698823967547924201…60283338837081403199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.069 × 10⁹⁷(98-digit number)

20698823967547924201…60283338837081403201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #56,955

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