Block #1,054,661

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2015, 12:17:07 PM · Difficulty 10.7278 · 5,741,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7361e09c176ae80b62609ba3fa73db1a78f0b7989c538a3aee467e715d3dba7c

View on Chainz ↗

Height

#1,054,661

Difficulty

10.727836

Transactions

Size

1.29 KB

Version

Bits

0aba5376

Nonce

1,518,856,548

Timestamp

5/11/2015, 12:17:07 PM

Confirmations

5,741,221

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

15c306547f7e88714ab6684eba173eebe859438f91ae095989a832c66bc4772a

Transactions (4)

Coinbasee6cb7958e806db…3696802a59631f

1 in → 1 out8.7100 XPM116 B

ANSXnLY2…Sd25TjkD

4e756d1d958f58…f1e54b92c7c1a2

2 in → 2 out11.1454 XPM373 B

AYrP9XRi…YHqRH7Xq AdUwqsJC…kyCDagPM

4395846af5b0a2…41e61a7fd6de87

2 in → 2 out16.3100 XPM374 B

Ae9drWdk…FnLTm9Pn AWA5Tca5…v6XhHWhQ

6deb8b67d8f5a4…dd9a17511367bf

2 in → 2 out0.5509 XPM372 B

Aeie6B9y…7FyCzXwj AafHMBZ3…rqiaCZAR

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.

1.662 × 10⁹⁸(99-digit number)

16626631738307355896…32783407677873971199

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

1.662 × 10⁹⁸(99-digit number)

16626631738307355896…32783407677873971199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.662 × 10⁹⁸(99-digit number)

16626631738307355896…32783407677873971201

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

3.325 × 10⁹⁸(99-digit number)

33253263476614711792…65566815355747942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.325 × 10⁹⁸(99-digit number)

33253263476614711792…65566815355747942401

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

6.650 × 10⁹⁸(99-digit number)

66506526953229423585…31133630711495884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.650 × 10⁹⁸(99-digit number)

66506526953229423585…31133630711495884801

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

1.330 × 10⁹⁹(100-digit number)

13301305390645884717…62267261422991769599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.330 × 10⁹⁹(100-digit number)

13301305390645884717…62267261422991769601

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

2.660 × 10⁹⁹(100-digit number)

26602610781291769434…24534522845983539199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.660 × 10⁹⁹(100-digit number)

26602610781291769434…24534522845983539201

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