Block #1,196,113

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/16/2015, 5:23:18 AM · Difficulty 10.8315 · 5,619,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bff8a6135b3f25c202d0ff09924d724e2e5f9758ba5a9503bfd2f4aff74aeca

View on Chainz ↗

Height

#1,196,113

Difficulty

10.831453

Transactions

Size

1.66 KB

Version

Bits

0ad4da1e

Nonce

2,328,079,618

Timestamp

8/16/2015, 5:23:18 AM

Confirmations

5,619,932

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

dc2a4ffaeddc1a8aa22a0880297d8fae8b3f478bfb181bb78590d7f37e4b2fb1

Transactions (3)

Coinbase34f2924f17596c…75437518ff53cb

1 in → 1 out8.5400 XPM116 B

AJCEY9yy…tg97E6zm

85321d7131456f…d452976b130e1b

6 in → 2 out25.3357 XPM967 B

AK9LxQQh…h24pctRm ARMAcSqc…qGGkYD5W

4dd3d4908649a7…a017774fe10390

3 in → 2 out1.0397 XPM524 B

AMjSGRKB…NLQuhj7g AbENQqzb…et8panq7

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.

1.235 × 10⁹⁷(98-digit number)

12358695421436692198…58469480260380206079

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

1.235 × 10⁹⁷(98-digit number)

12358695421436692198…58469480260380206079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.235 × 10⁹⁷(98-digit number)

12358695421436692198…58469480260380206081

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

2.471 × 10⁹⁷(98-digit number)

24717390842873384396…16938960520760412159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.471 × 10⁹⁷(98-digit number)

24717390842873384396…16938960520760412161

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

4.943 × 10⁹⁷(98-digit number)

49434781685746768793…33877921041520824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.943 × 10⁹⁷(98-digit number)

49434781685746768793…33877921041520824321

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

9.886 × 10⁹⁷(98-digit number)

98869563371493537586…67755842083041648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.886 × 10⁹⁷(98-digit number)

98869563371493537586…67755842083041648641

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

1.977 × 10⁹⁸(99-digit number)

19773912674298707517…35511684166083297279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.977 × 10⁹⁸(99-digit number)

19773912674298707517…35511684166083297281

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 #1,196,113

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