Block #2,402,180

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2017, 5:05:50 AM · Difficulty 10.8914 · 4,437,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ff3133657d4ec66b71d2fbb08b4c9771b30b5560cb9729bd3a203db2a160738

View on Chainz ↗

Height

#2,402,180

Difficulty

10.891430

Transactions

Size

9.24 KB

Version

Bits

0ae434c4

Nonce

1,292,174,723

Timestamp

11/30/2017, 5:05:50 AM

Confirmations

4,437,212

Mined by

⛏️ P2SHAdbzLVCkm3javteEo1KqqLbUs7SrGSGVZa

Merkle Root

487b8a47547a63bad988fada5da214712f8f8068a7efa631c3c1c00220177681

Transactions (2)

Coinbasea7bc38e23cfec6…1388f9a50a9b5f

1 in → 1 out8.5200 XPM109 B

AdbzLVCk…SrGSGVZa

a0213c8c07ea8e…b166a18487dbc2

62 in → 2 out461.5860 XPM9.04 KB

AU5bsQFi…RA19fWTB APdbDpvW…13WJV1sW

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.

1.205 × 10⁹⁶(97-digit number)

12059033834242769237…01309186627161456639

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

1.205 × 10⁹⁶(97-digit number)

12059033834242769237…01309186627161456639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.205 × 10⁹⁶(97-digit number)

12059033834242769237…01309186627161456641

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

2.411 × 10⁹⁶(97-digit number)

24118067668485538474…02618373254322913279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.411 × 10⁹⁶(97-digit number)

24118067668485538474…02618373254322913281

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

4.823 × 10⁹⁶(97-digit number)

48236135336971076948…05236746508645826559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.823 × 10⁹⁶(97-digit number)

48236135336971076948…05236746508645826561

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

9.647 × 10⁹⁶(97-digit number)

96472270673942153896…10473493017291653119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.647 × 10⁹⁶(97-digit number)

96472270673942153896…10473493017291653121

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

1.929 × 10⁹⁷(98-digit number)

19294454134788430779…20946986034583306239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.929 × 10⁹⁷(98-digit number)

19294454134788430779…20946986034583306241

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 #2,402,180

Cookie Preferences