Block #277,868

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 6:07:03 PM · Difficulty 9.9675 · 6,546,765 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62626e7ba41667e5b913f675fbb29b32392ceb673731ef80ff428b22caa9153f

View on Chainz ↗

Height

#277,868

Difficulty

9.967466

Transactions

Size

1.21 KB

Version

Bits

09f7abe1

Nonce

111,597

Timestamp

11/27/2013, 6:07:03 PM

Confirmations

6,546,765

Mined by

⛏️ P2SHAKCRCCETW8FUumyspNEmHXiVqDqxdRnend

Merkle Root

a4f3ebc574b55cf84579df2dddbe7ae106d4a4969ce39d7c3383313b14227aef

Transactions (3)

Coinbase366928bde08134…4f3b8d53630b64

1 in → 1 out10.0700 XPM109 B

AKCRCCET…qxdRnend

d0565ad1db9723…a71703a3e7298f

5 in → 2 out50.3800 XPM814 B

AYwj6bHa…DRzFPPqn ALyYSWSx…DQihbEze

e545a8cd576863…69f79890a6d1b6

1 in → 2 out3.6007 XPM226 B

AWHqSsod…S114Gc1Y AJvWDS3i…6czkdhQo

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.

9.209 × 10⁹⁴(95-digit number)

92093625935778145470…82472965714904431429

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

9.209 × 10⁹⁴(95-digit number)

92093625935778145470…82472965714904431429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.209 × 10⁹⁴(95-digit number)

92093625935778145470…82472965714904431431

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

1.841 × 10⁹⁵(96-digit number)

18418725187155629094…64945931429808862859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.841 × 10⁹⁵(96-digit number)

18418725187155629094…64945931429808862861

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

3.683 × 10⁹⁵(96-digit number)

36837450374311258188…29891862859617725719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.683 × 10⁹⁵(96-digit number)

36837450374311258188…29891862859617725721

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

7.367 × 10⁹⁵(96-digit number)

73674900748622516376…59783725719235451439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.367 × 10⁹⁵(96-digit number)

73674900748622516376…59783725719235451441

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

1.473 × 10⁹⁶(97-digit number)

14734980149724503275…19567451438470902879

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 #277,868

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