Block #1,181,217

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/3/2015, 5:02:04 AM · Difficulty 10.9211 · 5,657,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acd6ae2e907d8e6bde476f688a56aaf9a0fa597b41339d2b28bd7f9120144b7e

View on Chainz ↗

Height

#1,181,217

Difficulty

10.921106

Transactions

Size

18.62 KB

Version

Bits

0aebcd95

Nonce

2,984,075

Timestamp

8/3/2015, 5:02:04 AM

Confirmations

5,657,143

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

43c25447324480e500dea7068ffe857882bc4266b551479cd8995d26d8f5bf95

Transactions (2)

Coinbase3b6996ed1dcd9c…5ecd9786c50cde

1 in → 1 out8.6300 XPM116 B

AJCEY9yy…tg97E6zm

85c3f7564f75bb…e81ae3936d0620

127 in → 2 out1000.0005 XPM18.42 KB

AGTkgeWe…ck6rj3Cx AU48aYi5…4TvC7xu3

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.

2.039 × 10⁹⁸(99-digit number)

20392769460997773599…25331748207705538559

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

2.039 × 10⁹⁸(99-digit number)

20392769460997773599…25331748207705538559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.039 × 10⁹⁸(99-digit number)

20392769460997773599…25331748207705538561

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

4.078 × 10⁹⁸(99-digit number)

40785538921995547199…50663496415411077119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.078 × 10⁹⁸(99-digit number)

40785538921995547199…50663496415411077121

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

8.157 × 10⁹⁸(99-digit number)

81571077843991094398…01326992830822154239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.157 × 10⁹⁸(99-digit number)

81571077843991094398…01326992830822154241

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

1.631 × 10⁹⁹(100-digit number)

16314215568798218879…02653985661644308479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.631 × 10⁹⁹(100-digit number)

16314215568798218879…02653985661644308481

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

3.262 × 10⁹⁹(100-digit number)

32628431137596437759…05307971323288616959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.262 × 10⁹⁹(100-digit number)

32628431137596437759…05307971323288616961

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 #1,181,217

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