Block #1,090,716

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/5/2015, 11:37:24 AM · Difficulty 10.7342 · 5,711,914 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d29a20e12b6a6e2b68448315b7a71853a2b054d47b09d1a4e04ec4f2b7bcd9ea

View on Chainz ↗

Height

#1,090,716

Difficulty

10.734224

Transactions

Size

882 B

Version

Bits

0abbf617

Nonce

143,786,880

Timestamp

6/5/2015, 11:37:24 AM

Confirmations

5,711,914

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

96e0be8f11175115ba3d5d4860a860c95587c2969c9fa133c9692f84e7140003

Transactions (4)

Coinbase9c1e84da25fe91…c7e6ddabf8f77d

1 in → 1 out8.7000 XPM116 B

AJCEY9yy…tg97E6zm

41470499459cdb…6024f968434367

1 in → 2 out676.6074 XPM225 B

AGzX6zrq…2sUqUFQZ ARv4nDCp…nMVse715

d8c236c6b90373…89f9ad0615dd82

1 in → 2 out360.1662 XPM226 B

ALtrqaCi…P2vm2DFL AcdVU5yx…QVsWFgWB

206ec0bc1eaa39…61ef22f11357c8

1 in → 2 out50.1367 XPM225 B

AX9TVCAo…RC2d4HUr AKTd6ocn…Ewwo3nj2

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.

9.447 × 10⁹⁴(95-digit number)

94478741480063943028…10730234390243573439

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

9.447 × 10⁹⁴(95-digit number)

94478741480063943028…10730234390243573439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.447 × 10⁹⁴(95-digit number)

94478741480063943028…10730234390243573441

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

1.889 × 10⁹⁵(96-digit number)

18895748296012788605…21460468780487146879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.889 × 10⁹⁵(96-digit number)

18895748296012788605…21460468780487146881

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

3.779 × 10⁹⁵(96-digit number)

37791496592025577211…42920937560974293759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.779 × 10⁹⁵(96-digit number)

37791496592025577211…42920937560974293761

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

7.558 × 10⁹⁵(96-digit number)

75582993184051154422…85841875121948587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.558 × 10⁹⁵(96-digit number)

75582993184051154422…85841875121948587521

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

1.511 × 10⁹⁶(97-digit number)

15116598636810230884…71683750243897175039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.511 × 10⁹⁶(97-digit number)

15116598636810230884…71683750243897175041

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

3.023 × 10⁹⁶(97-digit number)

30233197273620461769…43367500487794350079

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