Block #2,563,078

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/13/2018, 1:33:01 AM · Difficulty 10.9930 · 4,268,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdab12aed7ab151474a60c9a517fc144c9cd0b2e8f403b4d78383e93fb96b400

View on Chainz ↗

Height

#2,563,078

Difficulty

10.992955

Transactions

Size

1.14 KB

Version

Bits

0afe3246

Nonce

845,642,080

Timestamp

3/13/2018, 1:33:01 AM

Confirmations

4,268,258

Mined by

⛏️ P2SHAdWXyGEaapAQ9mGVcmBwQbaVBiVd1Bn4pu

Merkle Root

62fda5927a7b158ce66094a26f8a0534ebeb72f746fea671281831b4f9fd32a7

Transactions (2)

Coinbase4716c51a77e344…f7dda0fedcaa5c

1 in → 1 out8.2700 XPM110 B

AdWXyGEa…Vd1Bn4pu

f96d5c5f8475d7…13d32b43e837eb

6 in → 2 out61.6551 XPM967 B

AbVbTAsM…jFVApoB8 AGfBoQRq…gmFEsxtU

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.

1.897 × 10⁹²(93-digit number)

18975999748247030848…14631886363282303999

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

1.897 × 10⁹²(93-digit number)

18975999748247030848…14631886363282303999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.897 × 10⁹²(93-digit number)

18975999748247030848…14631886363282304001

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

3.795 × 10⁹²(93-digit number)

37951999496494061696…29263772726564607999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.795 × 10⁹²(93-digit number)

37951999496494061696…29263772726564608001

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

7.590 × 10⁹²(93-digit number)

75903998992988123392…58527545453129215999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.590 × 10⁹²(93-digit number)

75903998992988123392…58527545453129216001

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

1.518 × 10⁹³(94-digit number)

15180799798597624678…17055090906258431999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.518 × 10⁹³(94-digit number)

15180799798597624678…17055090906258432001

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

3.036 × 10⁹³(94-digit number)

30361599597195249357…34110181812516863999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.036 × 10⁹³(94-digit number)

30361599597195249357…34110181812516864001

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

6.072 × 10⁹³(94-digit number)

60723199194390498714…68220363625033727999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,563,078

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