Block #277,624

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 3:44:32 PM · Difficulty 9.9668 · 6,515,078 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d0df5bc950ec7755b09ce41bb2f01fc141277fba8806c7b71d653d5a70efe091

View on Chainz ↗

Height

#277,624

Difficulty

9.966789

Transactions

Size

1.14 KB

Version

Bits

09f77f7c

Nonce

26,844

Timestamp

11/27/2013, 3:44:32 PM

Confirmations

6,515,078

Merkle Root

09f0bf9ad7201d3fd430e1d3bd704666836a72cb992afd7a8b8706060c2e6362

Transactions (2)

Coinbase8920feb7d8e70e…e8ef38649a47b6

1 in → 1 out10.0500 XPM97 B

AYSTY5gD…my21Gwsc

0579b9775c4bd1…1abcc469d86683

5 in → 12 out50.3911 XPM986 B

AKE6AX8q…V5iL8L3E AX2gzk4S…d2GsT5fq AMUH1Z1t…Q1XW99zU AP45oVsh…FvbwvLrG AGN47MX3…rXJKHoga

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.

9.192 × 10⁸⁸(89-digit number)

91928504514559919241…61368728258645320639

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

9.192 × 10⁸⁸(89-digit number)

91928504514559919241…61368728258645320639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.192 × 10⁸⁸(89-digit number)

91928504514559919241…61368728258645320641

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

1.838 × 10⁸⁹(90-digit number)

18385700902911983848…22737456517290641279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.838 × 10⁸⁹(90-digit number)

18385700902911983848…22737456517290641281

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

3.677 × 10⁸⁹(90-digit number)

36771401805823967696…45474913034581282559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.677 × 10⁸⁹(90-digit number)

36771401805823967696…45474913034581282561

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

7.354 × 10⁸⁹(90-digit number)

73542803611647935393…90949826069162565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.354 × 10⁸⁹(90-digit number)

73542803611647935393…90949826069162565121

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

1.470 × 10⁹⁰(91-digit number)

14708560722329587078…81899652138325130239

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