Block #1,246,738

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/21/2015, 6:05:56 PM · Difficulty 10.7524 · 5,580,239 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e69bb872a047ef6473b337c561ef92471b83411bc96901d809f654b5fab545e3

View on Chainz ↗

Height

#1,246,738

Difficulty

10.752437

Transactions

Size

1.95 KB

Version

Bits

0ac09fb0

Nonce

724,947,270

Timestamp

9/21/2015, 6:05:56 PM

Confirmations

5,580,239

Mined by

⛏️ P2SHASUEyfvtDncfiEHp83aCCPEYy9bY3CgPJR

Merkle Root

0e53d89407077662f98f9e1a0c66ea8860bbb90226683a0678f9dae01ea5773e

Transactions (5)

Coinbasedb717c4a64a37c…e9e321487d1cd1

1 in → 1 out8.6800 XPM109 B

ASUEyfvt…bY3CgPJR

2427950b2d0053…15448081602368

2 in → 2 out11.4272 XPM374 B

AFpqxhzb…mKpD37rB AZpeGnSF…4cbyDNBL

28c7e365bd565b…53c685a0111bf7

1 in → 2 out8.6200 XPM226 B

APaYVt8e…rPF99zd2 AGHqreGN…UKkz84uy

3101ee0cd4d9e8…bd3da11fd1537b

1 in → 24 out162.3391 XPM975 B

AYZPFrQF…UQ9rdPem ASkKNdmt…UtTKgcJe ASG21nzq…iMYaGLq3 Ab2i6LZQ…JMB6d2Mw AYRPhHU1…S577yeyi

e28692339859ad…15b77b953e2d52

1 in → 2 out5.2804 XPM226 B

AQzGsiip…LXYjaGXj ANhu7VoK…A3NjRTPq

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.

7.591 × 10⁹⁴(95-digit number)

75918025644066580813…68189299790755324399

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

7.591 × 10⁹⁴(95-digit number)

75918025644066580813…68189299790755324399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.591 × 10⁹⁴(95-digit number)

75918025644066580813…68189299790755324401

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

1.518 × 10⁹⁵(96-digit number)

15183605128813316162…36378599581510648799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.518 × 10⁹⁵(96-digit number)

15183605128813316162…36378599581510648801

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

3.036 × 10⁹⁵(96-digit number)

30367210257626632325…72757199163021297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.036 × 10⁹⁵(96-digit number)

30367210257626632325…72757199163021297601

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

6.073 × 10⁹⁵(96-digit number)

60734420515253264651…45514398326042595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.073 × 10⁹⁵(96-digit number)

60734420515253264651…45514398326042595201

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

1.214 × 10⁹⁶(97-digit number)

12146884103050652930…91028796652085190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.214 × 10⁹⁶(97-digit number)

12146884103050652930…91028796652085190401

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 #1,246,738

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