Block #2,701,125

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 6/11/2018, 4:46:33 PM · Difficulty 11.6346 · 4,140,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07e1d2f53efbfd0a673539118d3a2c390091ae36a42b39e4e150e8ea1780d214

View on Chainz ↗

Height

#2,701,125

Difficulty

11.634592

Transactions

Size

880 B

Version

Bits

0ba274a5

Nonce

2,097,350,995

Timestamp

6/11/2018, 4:46:33 PM

Confirmations

4,140,455

Mined by

⛏️ P2SHAVqXCRd8pxqyVSDu6rbn8cLM83DrsqtsVP

Merkle Root

c64378dc932a50e014adcf0a3cc8d673eeec9a4bb81827fb5dc5347c584c528a

Transactions (4)

Coinbasede88f42b26f005…048828e7bad2f8

1 in → 1 out7.4100 XPM110 B

AVqXCRd8…DrsqtsVP

b12d88fd76c4bd…1bda9bc1d72d31

1 in → 2 out51.5795 XPM226 B

AVKDZVxB…UzZJJTMr AHSWpUrB…aKSHiDiv

f2bc0f2a57520e…81bb270eec040f

1 in → 2 out41.5695 XPM227 B

AUdiN3Tx…5h9rGmyB APVKWthF…PMMxwRoz

aaa244be8b85f1…8a780269f03b92

1 in → 2 out31.5595 XPM226 B

AKfN5ELc…A3YNDXZ8 AS9fAEH9…pbhXm68T

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.

7.059 × 10⁹⁶(97-digit number)

70597832977932665447…29194257250262302719

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

7.059 × 10⁹⁶(97-digit number)

70597832977932665447…29194257250262302719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.059 × 10⁹⁶(97-digit number)

70597832977932665447…29194257250262302721

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

1.411 × 10⁹⁷(98-digit number)

14119566595586533089…58388514500524605439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.411 × 10⁹⁷(98-digit number)

14119566595586533089…58388514500524605441

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

2.823 × 10⁹⁷(98-digit number)

28239133191173066179…16777029001049210879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.823 × 10⁹⁷(98-digit number)

28239133191173066179…16777029001049210881

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

5.647 × 10⁹⁷(98-digit number)

56478266382346132358…33554058002098421759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.647 × 10⁹⁷(98-digit number)

56478266382346132358…33554058002098421761

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

1.129 × 10⁹⁸(99-digit number)

11295653276469226471…67108116004196843519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.129 × 10⁹⁸(99-digit number)

11295653276469226471…67108116004196843521

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

2.259 × 10⁹⁸(99-digit number)

22591306552938452943…34216232008393687039

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.259 × 10⁹⁸(99-digit number)

22591306552938452943…34216232008393687041

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,701,125

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