Block #58,753

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 10:25:56 PM · Difficulty 8.9615 · 6,748,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0056b08bf6b27c8a2a5b658bd5011c7c3e60d9a6f4030c0151a8004ed8dc8268

View on Chainz ↗

Height

#58,753

Difficulty

8.961548

Transactions

Size

11.44 KB

Version

Bits

08f627fc

Nonce

785

Timestamp

7/17/2013, 10:25:56 PM

Confirmations

6,748,384

Mined by

⛏️ P2SHARABMtFeApz7qYVC6tnpxfoVGEtan66YWt

Merkle Root

e64db5df55fa550d679553348642df2f37bf2e47674fb21bbcbde381f872738a

Transactions (2)

Coinbase3b21af130d987a…1756a867f4deca

1 in → 1 out12.5500 XPM110 B

ARABMtFe…tan66YWt

6a979d7d19ffc1…2cec6c4c658987

100 in → 2 out1253.1200 XPM11.24 KB

APBVxsMT…RAhyERWU ALjMex8i…QvzuMAXc

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.

4.573 × 10¹⁰¹(102-digit number)

45731621065474711406…07737930398552151979

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

4.573 × 10¹⁰¹(102-digit number)

45731621065474711406…07737930398552151979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.573 × 10¹⁰¹(102-digit number)

45731621065474711406…07737930398552151981

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

9.146 × 10¹⁰¹(102-digit number)

91463242130949422813…15475860797104303959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.146 × 10¹⁰¹(102-digit number)

91463242130949422813…15475860797104303961

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

1.829 × 10¹⁰²(103-digit number)

18292648426189884562…30951721594208607919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.829 × 10¹⁰²(103-digit number)

18292648426189884562…30951721594208607921

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

3.658 × 10¹⁰²(103-digit number)

36585296852379769125…61903443188417215839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.658 × 10¹⁰²(103-digit number)

36585296852379769125…61903443188417215841

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 #58,753

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