Block #278,108

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 8:37:44 PM · Difficulty 9.9680 · 6,513,518 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d887ef3b0eb40ae5a00c342265b06076e6179b5c5a9424c461225c59ccc186f

View on Chainz ↗

Height

#278,108

Difficulty

9.968036

Transactions

Size

1.15 KB

Version

Bits

09f7d136

Nonce

46,314

Timestamp

11/27/2013, 8:37:44 PM

Confirmations

6,513,518

Merkle Root

b2bc3e3ac9bf7d8d3301a471a99e19ef4920de3da1e17f8f86e363cc5766b3cc

Transactions (1)

Coinbaseb2bc3e3ac9bf7d…e363cc5766b3cc

1 in → 30 out10.0300 XPM1.06 KB

ALw8WzMm…sj2uYfgL AbiApRgN…g8QuFUwL AWXYBWKP…qQAoisBJ AJzWx2VD…j4ZSMit5 AJ9QW1VP…GmAJhvhc

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.

8.270 × 10⁹⁵(96-digit number)

82701314840743299544…25690893957976965949

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

8.270 × 10⁹⁵(96-digit number)

82701314840743299544…25690893957976965949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.270 × 10⁹⁵(96-digit number)

82701314840743299544…25690893957976965951

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

1.654 × 10⁹⁶(97-digit number)

16540262968148659908…51381787915953931899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.654 × 10⁹⁶(97-digit number)

16540262968148659908…51381787915953931901

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

3.308 × 10⁹⁶(97-digit number)

33080525936297319817…02763575831907863799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.308 × 10⁹⁶(97-digit number)

33080525936297319817…02763575831907863801

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

6.616 × 10⁹⁶(97-digit number)

66161051872594639635…05527151663815727599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.616 × 10⁹⁶(97-digit number)

66161051872594639635…05527151663815727601

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

1.323 × 10⁹⁷(98-digit number)

13232210374518927927…11054303327631455199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.323 × 10⁹⁷(98-digit number)

13232210374518927927…11054303327631455201

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