Block #1,516,390

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2016, 8:03:42 PM · Difficulty 10.6027 · 5,290,312 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17761e31e6669847cc331ca3f28e10d222317315fc0ef390eaae241c29a333bc

View on Chainz ↗

Height

#1,516,390

Difficulty

10.602701

Transactions

Size

1.35 KB

Version

Bits

0a9a4a9b

Nonce

49,150,452

Timestamp

3/28/2016, 8:03:42 PM

Confirmations

5,290,312

Mined by

⛏️ P2SHAehLMckHUH1fCrmhPkn32KfQwYeXdZRza3

Merkle Root

158adf2db9eb92098c867aadc84d05b691eb514e707da2ac288145285b637832

Transactions (2)

Coinbase6c3cd10de6bbc8…e2a0ad3429843a

1 in → 1 out8.9000 XPM110 B

AehLMckH…eXdZRza3

bb9e401d3f573b…786e53abe1d54f

1 in → 30 out0.8198 XPM1.15 KB

ALzFBL53…tm4jtFxq AXYbDkbL…4TQCMiP8 AcM6tNwn…xo98kcUZ AFzJsByB…cv1Lf5CS AX3mouNr…NAsScmbG

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.

9.116 × 10⁹⁶(97-digit number)

91168546007379545897…43649388199135641599

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

9.116 × 10⁹⁶(97-digit number)

91168546007379545897…43649388199135641599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.116 × 10⁹⁶(97-digit number)

91168546007379545897…43649388199135641601

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

1.823 × 10⁹⁷(98-digit number)

18233709201475909179…87298776398271283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.823 × 10⁹⁷(98-digit number)

18233709201475909179…87298776398271283201

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

3.646 × 10⁹⁷(98-digit number)

36467418402951818358…74597552796542566399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.646 × 10⁹⁷(98-digit number)

36467418402951818358…74597552796542566401

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

7.293 × 10⁹⁷(98-digit number)

72934836805903636717…49195105593085132799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.293 × 10⁹⁷(98-digit number)

72934836805903636717…49195105593085132801

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

1.458 × 10⁹⁸(99-digit number)

14586967361180727343…98390211186170265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.458 × 10⁹⁸(99-digit number)

14586967361180727343…98390211186170265601

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 #1,516,390

Cookie Preferences