Block #276,702

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 7:13:55 AM · Difficulty 9.9639 · 6,527,077 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4778a884025f3a391179552fe2f8061e58788ccc2ed09bb94a6f055d97f20fbd

View on Chainz ↗

Height

#276,702

Difficulty

9.963937

Transactions

Size

582 B

Version

Bits

09f6c492

Nonce

22,154

Timestamp

11/27/2013, 7:13:55 AM

Confirmations

6,527,077

Mined by

⛏️ P2SHAQGNq8GozEfx7uwrLGgqDNDvZMUTLxnGUe

Merkle Root

c8fe36e94d30b709d3cf759b579a90a2884536df7680ab8ff9084f0ea9c7795c

Transactions (3)

Coinbase31e9f19d647981…41e21d81a2b647

1 in → 1 out10.0800 XPM109 B

AQGNq8Go…UTLxnGUe

9be68ffe92662d…c0c325f43533d0

1 in → 1 out10.0700 XPM158 B

AP5m76AJ…4WJREPW6

cce3ad001f3e65…0ea4ce8b02af6c

1 in → 2 out99.9900 XPM226 B

AMaQuMAU…PafbyuGF APZNhEkg…kjDuYau9

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.

5.058 × 10⁹²(93-digit number)

50580498736657509388…39957055076596963119

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

5.058 × 10⁹²(93-digit number)

50580498736657509388…39957055076596963119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.058 × 10⁹²(93-digit number)

50580498736657509388…39957055076596963121

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

1.011 × 10⁹³(94-digit number)

10116099747331501877…79914110153193926239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.011 × 10⁹³(94-digit number)

10116099747331501877…79914110153193926241

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

2.023 × 10⁹³(94-digit number)

20232199494663003755…59828220306387852479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.023 × 10⁹³(94-digit number)

20232199494663003755…59828220306387852481

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

4.046 × 10⁹³(94-digit number)

40464398989326007510…19656440612775704959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.046 × 10⁹³(94-digit number)

40464398989326007510…19656440612775704961

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

8.092 × 10⁹³(94-digit number)

80928797978652015021…39312881225551409919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.092 × 10⁹³(94-digit number)

80928797978652015021…39312881225551409921

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