Block #2,288,085

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/8/2017, 5:09:43 PM · Difficulty 10.9555 · 4,554,037 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07a8f13273d9129f0763b391d0b6687e9bd2eded52fb3a12889669ed822a14e7

View on Chainz ↗

Height

#2,288,085

Difficulty

10.955521

Transactions

Size

652 B

Version

Bits

0af49d01

Nonce

1,804,296,162

Timestamp

9/8/2017, 5:09:43 PM

Confirmations

4,554,037

Mined by

⛏️ P2SHAeGu8u6UmAi2qWFmh7fE25TwMmdFtib4ng

Merkle Root

d7b04ec500b6eeb86e1ac6f83adc01261178be048c3deeaeaefc8f2b45d76387

Transactions (3)

Coinbasec16ad1d74c1a86…70a6314ae2a3df

1 in → 1 out8.3400 XPM110 B

AeGu8u6U…dFtib4ng

b20dffbe35cc15…45e28b90cf7cd8

1 in → 2 out2862.5479 XPM226 B

AYjaivKf…1HHdiRbZ AVGB6XAz…EpZuCyJJ

0e6fcc82e283f7…4a4ba3af20a678

1 in → 2 out1247.7115 XPM225 B

AQmMKmSM…qsSQy3cC AUHSHBEc…FjkBCZvB

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.

1.243 × 10⁹⁷(98-digit number)

12437263386857004274…20707478330764492799

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

1.243 × 10⁹⁷(98-digit number)

12437263386857004274…20707478330764492799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.243 × 10⁹⁷(98-digit number)

12437263386857004274…20707478330764492801

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

2.487 × 10⁹⁷(98-digit number)

24874526773714008549…41414956661528985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.487 × 10⁹⁷(98-digit number)

24874526773714008549…41414956661528985601

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

4.974 × 10⁹⁷(98-digit number)

49749053547428017099…82829913323057971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.974 × 10⁹⁷(98-digit number)

49749053547428017099…82829913323057971201

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

9.949 × 10⁹⁷(98-digit number)

99498107094856034199…65659826646115942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.949 × 10⁹⁷(98-digit number)

99498107094856034199…65659826646115942401

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

1.989 × 10⁹⁸(99-digit number)

19899621418971206839…31319653292231884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.989 × 10⁹⁸(99-digit number)

19899621418971206839…31319653292231884801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.979 × 10⁹⁸(99-digit number)

39799242837942413679…62639306584463769599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,288,085

Cookie Preferences