Block #155,861

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 2:48:15 PM · Difficulty 9.8663 · 6,637,690 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b3fc4f128def9fb2f1b40f83a4e0cd6cd3b04ddbffb6f67a5f787732ea7966f

View on Chainz ↗

Height

#155,861

Difficulty

9.866316

Transactions

Size

198 B

Version

Bits

09ddc6e0

Nonce

127,165

Timestamp

9/8/2013, 2:48:15 PM

Confirmations

6,637,690

Merkle Root

588f10584d7dafa22c288e9b0b35ae2cb2d68a08addea9848145c5e6ae64c7fe

Transactions (1)

Coinbase588f10584d7daf…45c5e6ae64c7fe

1 in → 1 out10.2600 XPM109 B

AJn9y9Wv…G4raUX4o

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.

6.449 × 10⁹¹(92-digit number)

64490522704558806376…83036207703680128049

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

6.449 × 10⁹¹(92-digit number)

64490522704558806376…83036207703680128049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.449 × 10⁹¹(92-digit number)

64490522704558806376…83036207703680128051

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

1.289 × 10⁹²(93-digit number)

12898104540911761275…66072415407360256099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.289 × 10⁹²(93-digit number)

12898104540911761275…66072415407360256101

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

2.579 × 10⁹²(93-digit number)

25796209081823522550…32144830814720512199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.579 × 10⁹²(93-digit number)

25796209081823522550…32144830814720512201

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

5.159 × 10⁹²(93-digit number)

51592418163647045101…64289661629441024399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.159 × 10⁹²(93-digit number)

51592418163647045101…64289661629441024401

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

1.031 × 10⁹³(94-digit number)

10318483632729409020…28579323258882048799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.031 × 10⁹³(94-digit number)

10318483632729409020…28579323258882048801

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