Block #277,848

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 5:57:38 PM · Difficulty 9.9674 · 6,546,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4ba37850e4183fd3e12f9d893e5f3845324ca293d1726c2d46c5e7840a0d01fd

View on Chainz ↗

Height

#277,848

Difficulty

9.967402

Transactions

Size

1.37 KB

Version

Bits

09f7a7a8

Nonce

126,994

Timestamp

11/27/2013, 5:57:38 PM

Confirmations

6,546,651

Mined by

⛏️ P2SHARAMmN4VwTjoqJsTbXay48dbnxg6URFbf8

Merkle Root

19329fdb5a5b93722ba661369a6ead0fa7c5fe4d366c5993168a3a9ae503629d

Transactions (5)

Coinbase1e4f86fe195af4…52ad99dbaba872

1 in → 1 out10.0900 XPM110 B

ARAMmN4V…g6URFbf8

afbcc8bb8b5a50…e8fd623412698b

2 in → 2 out10.4034 XPM375 B

ASuoUi24…FwBoFbxd AZ1hatq8…81QEJbXC

6cde5597627428…82dfcd67de135b

1 in → 2 out6.9972 XPM227 B

AWjj66Kv…z6cTR8NB AWGQhzDN…RDYvugUy

861c6c8121dcfd…0949307eea3129

1 in → 2 out6.1939 XPM225 B

AaVFHFSq…bCnX1Bpw ALLJtA9p…xLkfJG4b

7b36bca1929f7b…b04d0a9f1d36fa

2 in → 2 out1.0976 XPM374 B

AMfzRkqz…sGWTzctV AdjriTcz…C2VftMon

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.

3.307 × 10⁹⁴(95-digit number)

33077358374112235088…79075783072580285439

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

3.307 × 10⁹⁴(95-digit number)

33077358374112235088…79075783072580285439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.307 × 10⁹⁴(95-digit number)

33077358374112235088…79075783072580285441

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

6.615 × 10⁹⁴(95-digit number)

66154716748224470176…58151566145160570879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.615 × 10⁹⁴(95-digit number)

66154716748224470176…58151566145160570881

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

1.323 × 10⁹⁵(96-digit number)

13230943349644894035…16303132290321141759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.323 × 10⁹⁵(96-digit number)

13230943349644894035…16303132290321141761

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

2.646 × 10⁹⁵(96-digit number)

26461886699289788070…32606264580642283519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.646 × 10⁹⁵(96-digit number)

26461886699289788070…32606264580642283521

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

5.292 × 10⁹⁵(96-digit number)

52923773398579576141…65212529161284567039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.292 × 10⁹⁵(96-digit number)

52923773398579576141…65212529161284567041

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

Block #277,848

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