Block #956,197

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2015, 9:21:18 PM · Difficulty 10.8904 · 5,886,113 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65dbdbbeb66bf318c1f874f9a974d6fd7b40ea254e13b8d21b35b27f84c39d89

View on Chainz ↗

Height

#956,197

Difficulty

10.890440

Transactions

Size

2.15 KB

Version

Bits

0ae3f3df

Nonce

43,432,741

Timestamp

2/28/2015, 9:21:18 PM

Confirmations

5,886,113

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9a5f1dad9403a4c11ab59e8ca1f2286b47f28f50a27fd2b4723a86fccc328644

Transactions (2)

Coinbase2638ee60456978…3012337422597b

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

34315afd546d29…cc1651df1f2430

13 in → 2 out260.4480 XPM1.95 KB

ALRuXegM…qhkfJpvU AUyeqafx…SJsMeGN4

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.

7.352 × 10⁹⁵(96-digit number)

73526857983486553253…23514994429010886559

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

7.352 × 10⁹⁵(96-digit number)

73526857983486553253…23514994429010886559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.352 × 10⁹⁵(96-digit number)

73526857983486553253…23514994429010886561

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

1.470 × 10⁹⁶(97-digit number)

14705371596697310650…47029988858021773119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.470 × 10⁹⁶(97-digit number)

14705371596697310650…47029988858021773121

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

2.941 × 10⁹⁶(97-digit number)

29410743193394621301…94059977716043546239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.941 × 10⁹⁶(97-digit number)

29410743193394621301…94059977716043546241

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

5.882 × 10⁹⁶(97-digit number)

58821486386789242602…88119955432087092479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.882 × 10⁹⁶(97-digit number)

58821486386789242602…88119955432087092481

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

1.176 × 10⁹⁷(98-digit number)

11764297277357848520…76239910864174184959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.176 × 10⁹⁷(98-digit number)

11764297277357848520…76239910864174184961

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 #956,197

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