Block #1,973,167

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/7/2017, 1:54:06 PM · Difficulty 10.7546 · 4,868,320 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

811708acd782c350d0f23f6b03b55e6616c89d0f8b0fe51c3d7cb7640445969f

View on Chainz ↗

Height

#1,973,167

Difficulty

10.754646

Transactions

Size

11.11 KB

Version

Bits

0ac13079

Nonce

1,448,787,380

Timestamp

2/7/2017, 1:54:06 PM

Confirmations

4,868,320

Mined by

⛏️ P2SHATj9so3RJBA736DKyWM1kicJjiUhe6DvFA

Merkle Root

0f808fd08ae30156dc98626c649cf170f96d68031c35399bdd4c0d33ed90731b

Transactions (2)

Coinbaseb27297505d292c…2fa243db0e9ab7

1 in → 1 out8.7500 XPM109 B

ATj9so3R…Uhe6DvFA

138c96831ed45d…32645d394f6d0b

75 in → 2 out1443.6140 XPM10.92 KB

ATx17Ltn…yMBSoAZi AdUbFbQ9…MXLm2P1G

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.

1.649 × 10⁹⁸(99-digit number)

16492090682203015275…85080773202277498879

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

1.649 × 10⁹⁸(99-digit number)

16492090682203015275…85080773202277498879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.649 × 10⁹⁸(99-digit number)

16492090682203015275…85080773202277498881

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

3.298 × 10⁹⁸(99-digit number)

32984181364406030551…70161546404554997759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.298 × 10⁹⁸(99-digit number)

32984181364406030551…70161546404554997761

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

6.596 × 10⁹⁸(99-digit number)

65968362728812061103…40323092809109995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.596 × 10⁹⁸(99-digit number)

65968362728812061103…40323092809109995521

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

1.319 × 10⁹⁹(100-digit number)

13193672545762412220…80646185618219991039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.319 × 10⁹⁹(100-digit number)

13193672545762412220…80646185618219991041

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

2.638 × 10⁹⁹(100-digit number)

26387345091524824441…61292371236439982079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.638 × 10⁹⁹(100-digit number)

26387345091524824441…61292371236439982081

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

5.277 × 10⁹⁹(100-digit number)

52774690183049648882…22584742472879964159

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 #1,973,167

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