Block #420,105

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 4:25:07 AM · Difficulty 10.3657 · 6,384,936 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed39ac3a8f6ba51055123da1c64a8bb3eb37d2643f952365e81bfef4393029cf

View on Chainz ↗

Height

#420,105

Difficulty

10.365657

Transactions

Size

1.05 KB

Version

Bits

0a5d9bb5

Nonce

12,399

Timestamp

2/26/2014, 4:25:07 AM

Confirmations

6,384,936

Mined by

⛏️ P2SHAT4me1AvZf8VyvR54NxSRAex8obz6JjojW

Merkle Root

baba8ebd68ceb52a3e9c36192c0496eaaf44a0f62c5db044d57f184e73d0e41a

Transactions (2)

Coinbase75d9ff8184e048…427bfe06936541

1 in → 1 out9.3000 XPM109 B

AT4me1Av…bz6JjojW

1a5a3afc70ca26…2e899d245b4738

4 in → 12 out36.9800 XPM877 B

ASrQShXk…SPHWQiVY AcpjiZSC…TNRJHCGa AY93ye7Z…x4X1phnT AJTZmWMz…K4xGSLcs AeKNrjNj…1NEq95Ta

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.

1.859 × 10¹⁰⁰(101-digit number)

18593986533170567539…03380850305840290959

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

1.859 × 10¹⁰⁰(101-digit number)

18593986533170567539…03380850305840290959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.859 × 10¹⁰⁰(101-digit number)

18593986533170567539…03380850305840290961

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

3.718 × 10¹⁰⁰(101-digit number)

37187973066341135078…06761700611680581919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.718 × 10¹⁰⁰(101-digit number)

37187973066341135078…06761700611680581921

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

7.437 × 10¹⁰⁰(101-digit number)

74375946132682270156…13523401223361163839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.437 × 10¹⁰⁰(101-digit number)

74375946132682270156…13523401223361163841

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

1.487 × 10¹⁰¹(102-digit number)

14875189226536454031…27046802446722327679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.487 × 10¹⁰¹(102-digit number)

14875189226536454031…27046802446722327681

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

2.975 × 10¹⁰¹(102-digit number)

29750378453072908062…54093604893444655359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.975 × 10¹⁰¹(102-digit number)

29750378453072908062…54093604893444655361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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