Block #2,871,534

TWNLength 13★★★★★

Bi-Twin Chain · Discovered 10/7/2018, 6:47:13 PM · Difficulty 11.6665 · 3,970,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

90d0562ff6d37f0ec48a146699b171dd8054ddb1fe3e8d00c3e6792cd95ce838

View on Chainz ↗

Height

#2,871,534

Difficulty

11.666512

Transactions

Size

3.26 KB

Version

Bits

0baaa090

Nonce

467,422,888

Timestamp

10/7/2018, 6:47:13 PM

Confirmations

3,970,131

Mined by

⛏️ P2SHATvXYFtvhKhWkhP2eamhfoT81ZyxNpdoz2

Merkle Root

1611bd607f62beb78da01702ad1a5f8c8f222f6e47f7b300421a1af1ae970e40

Transactions (5)

Coinbase6696cfa53808f0…fabe922aac646a

1 in → 1 out7.3900 XPM110 B

ATvXYFtv…yxNpdoz2

7119937cd58e13…7d8f2a792ca3f9

17 in → 2 out100.5452 XPM2.11 KB

Ae1Qd1xa…4Jb4ropT AZrinwUb…sQussKcD

f29da0f1554b44…a21d8df9183324

2 in → 2 out14.6500 XPM307 B

AJi44Krn…u6BDha8s AXCz3i15…bd3tZodd

e5ebb056124c9a…de3208fcac92b2

2 in → 2 out11.9700 XPM339 B

APVKWthF…PMMxwRoz AVtYhomt…kjdYh4u2

ee1be51828a53a…3cd5ac15bc5a78

2 in → 2 out11.9700 XPM340 B

AQ7S9cWe…rDsLcCRa AHgBuNwX…h4iEV3bH

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.

5.125 × 10⁹⁷(98-digit number)

51257850804586303476…75662721679410626559

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

5.125 × 10⁹⁷(98-digit number)

51257850804586303476…75662721679410626559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.125 × 10⁹⁷(98-digit number)

51257850804586303476…75662721679410626561

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

1.025 × 10⁹⁸(99-digit number)

10251570160917260695…51325443358821253119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.025 × 10⁹⁸(99-digit number)

10251570160917260695…51325443358821253121

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

2.050 × 10⁹⁸(99-digit number)

20503140321834521390…02650886717642506239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.050 × 10⁹⁸(99-digit number)

20503140321834521390…02650886717642506241

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

4.100 × 10⁹⁸(99-digit number)

41006280643669042781…05301773435285012479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.100 × 10⁹⁸(99-digit number)

41006280643669042781…05301773435285012481

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

8.201 × 10⁹⁸(99-digit number)

82012561287338085562…10603546870570024959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.201 × 10⁹⁸(99-digit number)

82012561287338085562…10603546870570024961

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

1.640 × 10⁹⁹(100-digit number)

16402512257467617112…21207093741140049919

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.640 × 10⁹⁹(100-digit number)

16402512257467617112…21207093741140049921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

Level 6 — Twin Prime Pair (2^6 × origin ± 1)

2^6 × origin − 1

3.280 × 10⁹⁹(100-digit number)

32805024514935234224…42414187482280099839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 13 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

LegendaryChain length 13

Roughly 1 in 100,000 blocks. Extremely rare — celebrated by the community.

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 #2,871,534

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