Block #73,157

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 4:17:02 AM · Difficulty 8.9946 · 6,721,029 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3b57caa41ac3dcd869092b22b8e34f740295d294da35b1863f2b08b9c9aadcb1

View on Chainz ↗

Height

#73,157

Difficulty

8.994619

Transactions

Size

1.42 KB

Version

Bits

08fe9f53

Nonce

397

Timestamp

7/21/2013, 4:17:02 AM

Confirmations

6,721,029

Merkle Root

b721e35c320ce8c7499d1264660cfc0836a60ddf33fa07bb4164f81dd0ceb58b

Transactions (2)

Coinbaseab30865edecc78…c6e082e4b53dcc

1 in → 1 out12.3600 XPM110 B

AVzQ3Nvc…3tozGjpc

2a50edd3e2a09c…722086ecdcba83

10 in → 2 out112.1300 XPM1.22 KB

AJbWaZ4E…NcyR231j AakWTnji…NVBZri5U

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.

6.969 × 10⁹⁷(98-digit number)

69692338328424112580…14639930508140988899

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

6.969 × 10⁹⁷(98-digit number)

69692338328424112580…14639930508140988899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.969 × 10⁹⁷(98-digit number)

69692338328424112580…14639930508140988901

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

1.393 × 10⁹⁸(99-digit number)

13938467665684822516…29279861016281977799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.393 × 10⁹⁸(99-digit number)

13938467665684822516…29279861016281977801

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

2.787 × 10⁹⁸(99-digit number)

27876935331369645032…58559722032563955599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.787 × 10⁹⁸(99-digit number)

27876935331369645032…58559722032563955601

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

5.575 × 10⁹⁸(99-digit number)

55753870662739290064…17119444065127911199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.575 × 10⁹⁸(99-digit number)

55753870662739290064…17119444065127911201

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

1.115 × 10⁹⁹(100-digit number)

11150774132547858012…34238888130255822399

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